Succah 53b - Kal V'Chomer of Achitofel

The gemara tells a story where Dovid HaMelech was digging the שיתין for the beis hamikdash that bring the water down to the depths and was unsure whether he can erase Hashem's name to prevent the waters from flooding the world. Achitofel taught Dovid that a Kal V'chomer can be made from a Sotah, if to bring peace between a husband and wife the name of Hashem can be erased, then certainly to prevent the water from flooding the world it can be erased.

There seems to be a major question on this gemara. Why do we need a kal v'chomer from Sotah, it should be a simple halacha that pikuach nefesh pushes off all issurim in the Torah? It is fair to assume that flooding the entire world would be an issue of pikuach nefesh, so it should have been obvious to Dovid that the name of Hashem can be erased to preven that?

I recall seeing in the sefer of Rav Peretz Steinberg on the Rambam that the issur of erasing the name of Hashem is connected to avoda zara because the torah commands us to destroy avoda zara and then says לא תעשון כן לה' אלקיכם. Since it is connected to avoda zara, there would be no heter of pikuach nefesh. That is why Achitofel had to darshan a special limud from Sotah to permit it.

I would suggest a different answer. Surely pikuach nefesh would permit the name of Hashem to be erased. The problem was that Dovid held like the opinions in Yoma 85b that only definite pikuach nefesh pushes off issurim, but safeik pikuach nefesh does not (which the gemara considers to be the advantage of וחי בהם because only that source would teach that even safeik pikuach nefesh is docheh issurim). Dovid knew that it wasn't clear whether erasing the name of Hashem by throwing the piece of clay into the water would be an effective method of stopping the flood. It was only a safeik and therefore he held it could not be done. However, Achitofel introduced a kal v'chomer from Sotah. By Sotah the right to erase Hashem's name to bring peace is also only a safeik. If she is indeed guilty it will not bring peace, yet it was permitted because of the chance that she is innocent and the erasing of Hashem's name will restore their shalom bayis. This is very meduyak in rashi - לעשות שלום בין איש לאשתו- לבדוק את הסוטה ואם טהורה היא יהא שלום ביניהם, only if she is actually innocent will it bring peace. Therefore, learning a kal v'chomer from sotah would be an effective way to show that even for a safeik of restoring peace the name of Hashem could be erased. That is why we need the source from Sotah and can't rely on the standard pikuach nefesh approach.

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On another note- there is a major historical flaw in the story. Achitofel died after advising Avshalom and Avshalom preferring the advice of Chushai Ha'archi, which happened prior to Dovid purchasing the land for the Beis Hamikdash from Aravna HaYevusi. So, when Dovid was digging the שיתין, Achitofel should have been long dead. See Rashi in Makos 11a.

Succah 46a - Making a Bracha on Seeing a Mitzvah

The gemara says that for Ner Chanukah there was a bracha of she'asa nissim instituted on the seeing of the mitzvah, even without actually performing the mitzvah. Rashi implies that so long as one has not yet lit ner chanukah, they make a bracha on the seeing of the ner lit by someone else, even if they intend to light themselves later that evening. Rashi in Shabbos is explicit about this. However, we follow the opinions that the bracha on seeing was only instituted for those who don't intend to light themselves, and don't have people in their household lighting for them.

Tosafos asks why chazal did not institute a bracha on seeing any other mitzvah, and only instituted a bracha for the seeing of Ner Chanukah. It seems that Rashi was also bothered by this question and tries to address it. Rashi writes - ורואה אותה בפתחי ישראל שמצוה להניח בפתח, צריך לברך על ראיה הראשונה. Rashi seems to add a superfluous line - שמצוה להניח בפתח. Simply, Rashi is just explaining how one happens to see the Ner lit by someone else when just passing by on the street. However, it seems to me that Rashi is trying to say that lighting in a way that it is visible from the street was part of the ikar takana of ner chanukah, therefore when one sees the ner chanukah of someone else, chazal instituted a special bracha. For other mitzvos where the publicizing was not part of the ikar takana, chazal were not mesakein a bracha on merely seeing it.

Tosafos offers three answers to this question. 1. Due to the חביבות הנס and inspiring love for the miracle, they instituted a bracha on the seeing of Ner Chanuka. This would not apply to mitzvos that don't directly represent a Neis. 2. Many people don't have homes of their own in which to light Ner Chanuka, therefore chazal instituted a method of connecting them to the mitzvah by making a bracha on the seeing of the candle. 3. It only makes sense to institute a bracha on the seeing, if when actually performing the mitzvah, one would also make that bracha. Since there is no bracha of שעשה נסים made on taking lulav and sitting in a Succah, there is no bracha made on the seeing of it.

Tosafos rejects the second answer by saying that it is difficult from mezuzah. Meaning, if chazal were worried about one who doesn't have a house being unable to perform this mitzvah and therefore instituted some connection to the mitzvah, namely to make a bracha on the seeing of the Ner, they should have instituted a bracha on seeing a mezuzah as well, to accommodate for those who don't have homes to hang a mezuzah.

This question of Tosafos is very difficult to understand. It seems that there is a fundamental distinction between mezuza and ner chanukah. One who doesn't have a house is patur from mezuzah. In other words, mezuza is a chovas ha'dor, an obligation on one who lives in a house. The house is the me'chayev in the mitzvah. Without a house there is no obligation to do the mitzvah at all. One is certainly not compelled to buy house to perform this mitzvah. However, the mitzvah of ner chanukah is a mitzvah on the individual, just that one needs a house to have a place to light. One who is missing a house is still technically obligated in the mitzvah, just that they have no ability to perform it. It is as if they are handcuffed to a pole and therefore unable to take lulav. Therefore, it would make sense that for such a situation chazal would institute a possibility to at least connect to the mitzvah and make a bracha on the seeing of the Ner.

Succah 42a - Intent Not To Be Yotzei

Tosafos 39a writes that one of the solutions to ensure that one is going to be making the bracha prior to performing the mitzvah of lulav is to intend to NOT be yotzei by lifting it up until after the bracha. Tosafos is confident that this works, since even according to the opinion that mitzvos don't require kavana, when one has intent explicitly NOT to be yotzei, he is not yotzei.

The Biur Halacha (cited in my sefer nasiach b'chukecha pg 129) writes that if one is accustomed to always counting sefira after tzeis hakochavim, and is asked by someone during bein hashmashos what night of the omer it is, even if they responded with the correct number they can count later with a bracha. The justification is that even if mitzvos don't require kavana, since this person always counts later, it is as if he is intending not to be yotzei when he tells his friend the correct number.

To extend this sevara one step further, perhaps one can argue that when one is accustomed to always doing a mitzvah with a bracha, until they actually make the bracha it is as if they were intending not to be yotzei. In other words, if the biur halacha is correct that we can look at the persons general practice to consider it as if he were intending not to be yotzei, we should be able to look at the absence of the bracha as an indication as well.

There is a clear proof from Tosafos that this is incorrect. The gemara on 42a struggles with how to find a case where a person is carrying out a lulav and will not be yotzei. Tosafos asks why don't we just say that he isn't yotzei since mitzvos require intent and he is not intending to be yotzei. Tosafos explains that since he isn't making a bracha now, it is clear that he is not intending to be yotzei. The implication of Tosafos is that according to the opinion who says that mitzvos do not require kavana, the gemara works out fine. But why don't we say that even according to the opinion that kavana is not necessary, he should not be yotzei by carrying it out. The rationale would be that since he is not making a bracha now, it is as if he intended explicitly NOT to be yotzei because his practice is to always do this mitzvah with a bracha. Clearly, Tosafos holds that although explicit intent to NOT be yotzei would work even according to the opinion that מצות אין צריכות כוונה, but by merely not making a bracha we CANNOT interpret his intent to be as if he were intending NOT to be yotzei. Tosafos assumes that if mitzvos don't require intent he would be yotzei, and that is why the gemara needs to struggle to find the case where he isn't yotzei.

Succah 31a - Making a Bracha on a Succah Based on Takanas Marish

The gemara tells a story of a woman who complained that the Rabbononin the house of the Reish Gelusa were sitting in a stolen Succah. Rav Nachman ignored her complaint because although the wood that was used for the succah was stolen, by building it into a Succah, they acquired it through תקנת מריש and only need to return the value of what they stole. The point of the gemara is that for the duration of Succos we consider any material built into a Succah to be as if it were built into a permanent structure like a house. Just as the Rabbonon made a תקנת השבים to say that a beam that was built into a house doesn't have to be disassembled and returned, they made the same takana by a Succah for the duration of Succos (but if the owner is willing to wait until after Succos and wants his wood back, then it must be returned).

The Takanas Marish is essentially a d'rabonon method of allowing the thief to acquire what was stolen without having to go through the technicalities of yiush and shinuy. If the wood would have actually undergone yiush and a shinuy ma'aseh or shinuy reshus, there would be a kinyan on it without any special takana d'rabonon, but the chiddush here is that although there is no technical kinyan, the person is koneh based on this takana and doesn't need to return the beam. It would seem that just as when one makes a kiyan d'oraysa based on yiush and shinuy, they can still not make a bracha on the succah (as tosafos 30a points out - שאני ברכה דאיכא נמי הזכרה לשם שמים).

However, the Mishna Berura (637:15) writes that based on the takanas marish one can even make a bracha. In the Sha'ar Hatziyun (21)  - דבודאי ריש גלותא ורבנן היו מברכין עליה גם כן, he indicates that the source is that the Rabbonon who were sitting in this Succah would not have sat in a Succah that they couldn't make a bracha on, therefore they were presumably making brachos. This seems to be a big chiddush. Simply, the takanas marish itself is a chiddush in that it applies to succah, and it would seem that it should be as good as a kinyan d'oraysa, not  better than a kinyan d'oraysa. The M.B. seems to understand that the takanas marish is more powerful than a kinyan doraysa of yiush and shinuy because it enables you to even make a bracha.

It seems to me that this issue is contingent on what the Rabbonon did with their תקנת מריש. Did they merely institute that it doesn't need to be returned once its used in a Succah just as if it were used in a house, but the heter for the mitzvah haba'ah b'aveira is the standard approach that whenever one is koneh prior to the mitzvah, it is not a problem of mitzvah haba'ah b'aveira. Based on this approach it should be exactly like the halacha when there is yiush and shinuy, one can be yotzei but NOT make a bracha. Or did the Rabbonon make a special takana to address the mitzvah ha'ba'ah b'aveira, meaning that they pretended as if there were never any beam stolen, just that the value is owed to the original owner. Based on this approach, it is as if there was no aveira done with the beam so that one can even make a bracha on the Succah.

It seems to me that this is contingent on a machlokes between the Ritvah and Tosafos in Gittin. The Ritvah writes הרי העצים האלו שסיכך בהם קנויים לו מדרבנן מתקנת מריש, ואין עליו אלא חוב דמיהם שחייב לבעלים, והרי הוא כחוב דעלמא ומשלך קרינא ביה, וליכא נמי משום מצוה הבאה בעבירה, דהא קנינהו מקמי מצוה. The Ritva seems to hold that the way around the mitzvah haba'ah b'aveira is that you are koneh the beam prior to the mitzvah, therefore the din should be the same as whenever you are koneh prior to the mitzvah that you can't make a bracha. However, Tosafos in Gittin 55a (d.h. mai) writes ובסוכה לא בעינן משלכם, ולא מפסלא אלא מפני מצוה הבאה בעבירה, וכי קניא בתקנתא דרבנן לא חשיב מצוה הבאה בעבירה. It is very meduyak from Tosafos at the end that only by the challah case where the right to use it was that he was koneh before the mitzvah are we machmir not to make a bracha, but not when the Rabbonon institute to view it as if there is no aveira done. Tosafos seems to hold that the way around the mitzvah haba'ah b'aveira is that the Rabbonon make a takana as if it were never stolen at all, therefore this should work to allow even the making of a bracha, as the M.B. paskens.

Succah 22b - Using a Succah in a Tree

The Mishna says that if one makes a Succah in a tree, it is kasher but one cannot use it on yom tov because there is an issur to climb up a tree on yom tov. The Sefas Emes points out that it would even be assur to climb the tree before yom tov and wait until yom tov starts. He proves that it would be a violation from the fact that R. Yehuda considers a Succah in a tree not fit for the 7 days of Succos. If it were possible to go up before yom tov, it should be considered fit for 7 days to at least use on chol hamoed.

Rashi writes that in addition to one using it on chol hamoed, if one used it on yom tov b'issur, they would fulfill their mitzvah of Succah. The Pri Megadim points out that this should be a mitzvah haba'ah b'aveira since the mitzvah is completely contingent on doing the aveirah. In my sefer, I pointed out that this Rashi may hold that there is no problem of mitzvah haba'ah ba'aveira when the aveira is only d'rabonon. Otherwise, it is very difficult to understands why one would be yotzei. Perhaps Rashi means to say that on a d'rabonon level it would be a mitzvah haba'ah ba'aveira, but on a d'oraysa level there is no aveira, therefore m'drabonon one is not yotzei, but m'doraysa one would be yotzei. The Mishna Berura (628:3) cites a machlokes between the pri megadim and bikurei yaakov whether one should use such a Succah if that is all they have. The Pri Megadim entertains that one can use the Succah to fulfill the mitzvah d'oraysa, whereas the bikurei yaakov says that the chachamim uprooted the mitzvah בשב ואל תעשה, which they have the authority to do. According to the Pri Megadim that one should actually use such a Succah to fulfill the d'oraysa, we can understand that Rashi means to say that one is yotzei m'doraysa, just not m'drabonon.

Succah 16a - Placing Sechach Before the Walls

The Rama (635) cites the Hagahos Maimonies that when one is building a succah they should be careful to first make the walls of the Succah so that at the time they place the sechach on top, the placing of the sechach will render it a kosher Succah. This seems to be against the gemara that says that as long as there is a חלל טפח when one placed down the גדיש, pile of hay, they can then be חוטט בגדיש (carve out a space in the pile) and it would be a kasher succah. In this case the sechach is being placed prior to the walls being formed, yet it is okay. The Rama deals with this question by qualifying the din  - ואם עשה טפח סמוך לסכך מותר לסכך קודם שיעשה שאר הדפנות כמו בחוטט בגדיש. Meaning, that so long as one has a 1 tefach wall at the time they place the sechach, it is permitted to construct or carve out the rest of the wall after placing the sechach. The justification for this is that the hagahos maimonies understands that the succah doesn't need to be kosher the moment the sechach is placed on top, rather the sechach must be placed on top of a succah that is considered to have walls, even if the walls are just a tefach.

The Magen Avrohom cites the Bach who says that it is only a din lichatchila, but bidieved even if one placed the sechach before forming the walls it would be kasher, and the Levush disagrees and holds that it is passul. The source of the Bach is a Rashi in the Mishna 16a that is cited by the Bach. Rashi describes one who is making the walls of the Succah מלמעלה למטה - שהתחיל לארוג המחיצה אצל הסכך ואורג ובא כלפי מטה. It seems from rashi that the sechach is already up on the Succah and he is starting to construct the walls "אצל הסכך", implying that as of yet there are no walls, yet by forming the walls, the Succah will be kasher. The Taz rejects this proof because Rashi is not intending to describe the sechach being on the succah, he is merely trying to describe the location where he is starting to make the wall, and that is near where the sechach would be. Rashi is not intending to say that the sechach is already there. Therefore, the Taz rules like the levush, against the Bach, and holds that if the sechach is placed before the walls are formed, the Succah will be passul m'doraysa.

To me it seems that although there may not be a proof from the Rashi cited by the Bach, there is another Rashi that clearly holds that the argues on the Hagahos Maimonies who is the source of this chumrah. The Hagahos Mamimonies must understand that the case where one piles a גדיש on a חלל טפח is where there are already walls that are a tefach in width on which he is putting the gadish, and then carving out the other 9 tefachim to form 10 tefach walls. According to this approach the focus should be on the fact that there was a tefach of wall that exists prior to the placing of the gadish (which serves as the sechach). However, when Rashi explains this gemara, he doesn't focus on the walls at all. Rashi seems to understand the the requirement of having a חלל טפח at the time that one places the gadish is because without airspace of a tefach, the gadish cannot qualify as sechach. It sounds from Rashi that even if there were no planks of wood under the gadish that can serve as walls, so long as the gadish will be lifted from the ground by a tefach and form a tefach of hollow space underneath, one can then be חוטט בגדיש to create 10 tefach walls. This is clear from Rashi who writes that the problem without a חלל טפח  is - דעכשיו נעשה שם סכך מאליו ולא היה עליו שם סכך מתחילה, and the solution of having a חלל טפח is -

נמצא שם סכך על אותו גדיש, וכשחוטט מלמטה למעלה עד שמגביה את החלל לשיעור גובה עשרה אין זו עשייתו שהרי אינו מתקן אלא הדפנות, ובדפנות לא אמרינן תעשה ולא מן העשוי

Rashi does not at all focus on whether or not the boards under the gadish that create a chalal tefach are placed in a way that they are fit to serve as walls. The entire focus is that the gadish be placed so that at the time it is placed, it creates a chalal tefach. So long as it creates a chalal tefach, the entire construction of the walls can take place AFTER the placing of the sechach. Being that this sugya is the source of the Hagahos Maimonies, and Rashi seems to understand the gemara differently and holds that there is no requirement for walls to exist at all prior to placing the sechach, there is no source for this din. This is all to develop the shitah of Rashi but l'ma'asah, we are bound by the Rama who paskens like the Hagahos Maimonies.

Succah 16b - Mechitzah HaMateres

Rashi learns that the prohibition of making an ohel only applies to using a curtain as a roof, but using a curtain as a wall is permitted. Rashi seems to hold that even if the mechitzah is functional to permit carrying, it can be made on shabbos. Tosafos disagrees with Rashi and writes that just as we find in the gemara that the third wall of the Succah which will be machshir the Succah cannot be made on Shabbos, any mechitzah hamateres cannot be made on shabbos. Tosafos holds that a mechitzah that is meant to permit carrying is also a mechitzah hamateres and cannot be made on shabbos. Based on Tosafos, the Rama 315:1 writes that one cannot make a mechitzah in front of a lit candle to permit having relations because that is also a מחיצה המתרת and is assur to make on shabbos. There is a gemara in Beitzah that seems to contradict this. The gemara 22a seems to hold that it is permissible to build a wall to block the light of a candle. The Taz writes on Hilchos Yom Tov (514) that if it is permitted to put out the candle, it would also be permitted to make a wall. However, the Chazon Ish (52:14) disagrees with the Taz. Even if it is permitted to put out the candle, it should be forbidden to put up a curtain. It would be similar to saying that since one can eat in  another Succah, they can put up a wall in this one. Why would the ability to put out the candle permit the making of the wall! The Chazon Ish explains that the answer is as the Magen Avrohom says. All one needs for a candle is to block the light, therefore the mechitzah that blocks a candle doesn't need to have status of a mechitza so long as it blocks the light. The mechitzah would be the equivalent to the candle going out which permits having relations without constructing a mechitzah hamateres. Based on the Magen Avrohom it comes out that if the mechitzah blocks out the light it would not be a mechitzah hamateres and be permitted, but if it doesn't block the light then it would only work because it is a mechitzah and therefore forbidden. The Chazon Ish continues that the Magen Avrohom also says that if one doesn't tie the curtain on the bottom, it will not be considered making a mechitzah since it can blow in the wind but the Chazon Ish disagrees and says that since it is being built in a house where there is no wind, it qualifies as a mechitzah even if it is not tied down.

Succah 10b - Osek B'mitzvah D'rabonon

The gemara cites a machlokes between R. Nachman  and R. Chisda regarding decorations that hang more than 4 tefachim below the roof, whether it invalidates the Succah. Although R. Chisda and Raba Bar Rav Huna held that it does invalidate the Succah, when they were travelling to visit the Reish Gelusa for the Yom Tov they slept in such a Succah. Their rationale was that although in their opinion the Succah is passul, they were שלוחי מצוה and therefore exempt from sleeping in a Succah. Rashi comments that they were considered shluchei mitzvah because they were going to greet their rebbi  - שלוחי מצוה אנן, להקביל פני ראש גולה, דחייב אדם להקביל פני רבו ברגל. It is unclear to me why rashi needs the additional phrase of דחייב אדם להקביל פני רבו ברגל. Does Rashi mean to say that since chazal instituted that one must visit his Rebbi on Yom Tov (Rosh Hashana 16), therefore it was considered a mitzvah to exempt from succah but had there not been a specific obligation to go then it would not exempt. Or does rashi mean to simply say that we see from there that there is a mitzvah involved in visiting one's rebbi so regardless of when goes to visit their rebbi they would be exempt from other mitzvos that come their way? It seems from Rashi that it was specifically because there was an obligation at that time to visit one's rebbi that they were able to go knowing that they would likely miss out on the mitzvah of succah, otherwise they should have waited and gone a different time.

In my sefer Nasiach B'Chukecha (pg. 63) I have a discussion whether we say עוסק במצוה דרבנן exempts one from a mitzvah d'oraysa. I quoted that Rav Eliyashiv cites our gemara as a proof that even a mitzvah d'rabonon exempts from mitzvah d'oraysa, because greeting one's Rebbi is only learned מדברי קבלה, yet it is apparently considered a mitzvah to exempt from Succah. Today I found that the Mitzpeh Eisan makes exactly the same point. He draws a parallel from the gemara in Sanhedrin 70 where the gemara says that if a ben sorer u'moreh eats meat that is assur m'drabonon he doesn't become a ben sorer u'moreh. The gemara explains that the pasuk says ואיננו שומע בקולנו, he doesn't listen to the voice of his parents implying that that is the only voice stopping him from eating the meat - לאפוקי האי דאף בקולו של מקום איננו שומע. Just as in that context we regard an issur d'rabonon to be like a d'oraysa and it doesn't qualify as קולנו, so too by osek b'mitzvah which is learned from בלכתך בדרך - בלכת דידך, to exclude a mitzvah, an mitzvah d'rabonon would also qualify as a mitzvah.
The Ya'avetz is medayek from Tosafos that they disagree with Rashi. Tosafos writes - שלוחי מצוה אנן, וכגון שהיו מתבטלים מן המצות אם היו מחזרין אחר סוכה אחרת, that the mitzvah they would have lost was not merely the mitzvah of greeting their rebbi, but other mitzvos. If greeting their rebbi was the only mitzvah they would have lost, they would not be exempt from succah. Tosafos implies that there were other mitzvos that were presumably d'oraysa that they would have lost out on, had they made the effort to sleep in a succah.

Nonetheless, in my sefer I pointed out that from this proof we only see that a mitzvah d'rabonon which is a kiyum of  a d'oraysa such as honoring a Rebbi, exempts from a d'oraysa mitzvah. But we still don't see that a pure d'rabonon which is not at all a kiyum of a d'oraysa would exempt from a d'oraysa obligation.

Succah 9a - "Old" Succah

There is a machlokes beis shamai and beis hillel regarding a succah made more than 30 days prior to succos. Beis Shamai holds that it is passul and Beis Hillel holds that it is kasher. The Mishna ends off by saying that if a Succah was built לשם חג, even if built from the beginning of the year it is kasher. Rashi says that the last line of the Mishna is only necessary for Beis Shamai because according to Beis Hillel it is kasher anyway. Tosafos on the other hand cites the Yerushalmi that holds that even Beis Hillel partially admits to Beis Shamai that if built not לשם חג more than 30 days prior to Succos it is necessary to be מחדש בה דבר, meaning to redo some amount of sechach spanning accross the width of the succah. Based on this Tosafos explains that the last line of the Mishna can fit with Beis Hillel as well. The advantage of constructing the Succah לשם חג is that he will not need to be מחדש בה דבר. Rashi seems to understand that the Bavli which makes no mention of this requirement within Beis Hillel would apparently hold that it is unnecessary to do anything. Since Beis Hillel holds that a Succah doesn't need to be built for the purpose of Succos, it would not be necessary to be mechadesh anything in the Succah.

According to Tosafos who holds that within Beis Hillel it would be necessary to be מחדש בה דבר if built too early and not לשם חג, it would seem that it would only be a d'rabonon requirement, not d'oraysa. The gemara is clear that Beis Hillel rejects the pesukim that Beis Shamai would use to indicate that a Succah needs to be built לשם חג. Therefore, even Beis Hillel would have no Torah source to demand being מחדש בה דבר, so apparently it would only be d'rabonon. The Mishna Berura (636:4) explains that the din of being מחדש בה דבר is not even an absolute din d'rabonon, it is just a mitzvah lichatchila so that one does not come to use something made as their permanent residence as their succah which would be a p'sul d'oraysa.

According to Tosafos we would require even by סוכת גנב"ך which was made for shade but not for Succos, that they be מחדש בה דבר. However, what would be the halacha for סוכת גנב"ך that is made within 30 days of Succos? How does the concept of סתמא לשמה work when it is not even being made by those who are obligated in the mitzvah? Would it even work for Succos that are built by those who are not obligated in the mitzvah and never heard of the mitzvah?

This would depend on how we understand the concept of סתמא לשמה. If the concept is based on the assumption that any Succah built within 30 days of Succos is assumed to be built for succos so even if the person didn't have explicit intent, we are confident that if we were to ask him he would confirm that would have been his intention. According to this approach, a Succah built by a goy even within 30 days one would need to be mechadesh something because for a goy there is no סתמא לשמה. But if we understand that concept similar to how the Steipler at the beginning of Zevachim and Dibros Moshe (Gittin heara 126 - pg. 544) in the context of a korban being סתמא לשמה, that there is an automatic infusion of לשמה since the korban is designated for that purpose, here too we can say that within 30 days of Succos it is automatically infused with lishma. In other words, is the סתמא לשמה a din in the gavra that we assume his subconsciousness would want it to be lishma (which would not apply for a goy) or is it a din in the z'man that anything built during that time assumes a status of built for the chag (which would apply even if a goy builds it). By Rashi citing the concept of שואלין ודורשין קודם לחג ל' יום as the reason we assume that within 30 days of succos it is סתמא לשמה, it seem that the latter approach that the z'man is automatically infused with kedusha is correct. Based on this approach it would not be necessary to be mechadesh something even in a סוכת גנב"ך. However, the Mishna Berura (536:4) citing the achronim takes for granted that one would need to be mechadesh something in a סוכת גנב"ך.

Succah 7b - Diras Keva

The gemara lists 8 Tanaim who hold that for a Succah we require a דירת קבע, a permanent dwelling and it is not sufficient to have a diras ara'i. Tosafos points out that it is unnecessary and impossible that each of the 8 opinions will hold of each other, and there is clearly discrepancy between them, but conceptually they all agree that on some level we demand דירת קבע.

For the most part, each of the opinions cited by the gemara seems to say that the succah MUST be built in a way that resembles a more permanent structure, like a house, rather than a temporary structure. Rashi's language is - דירת קבע: ראויה להשתמש קבוע ונראית כבית, fit for permanent use and looks like a house. Some opinions make demands in the size of the Succah, such as Rebbi who requires 4 amos and Beis Shamai who requires that it fit the person and his table. Some make a demand in the place of the succah such as Rabban Gamliel who says that it cannot be built on a boat or wagon. Some make a demand in the shape such as the Acheirim who say it cannot be built circular, and Rebbi Eliezer who says that it must have distinct walls and a distinct roof, and R. Yoshiya who says that the walls are as significant as the roof and must not allow too much sun in. Included in the list is also R. Shimon who demands that the Succah contain 4 walls (just that the third can be a tefach). The gemara 6b has two explanations for R. Shimon, one is that it learns from the words סוכת סוכת סוכות that a Succah must contain 4 walls, and another is the pasuk of וסוכה תהיה לצל יומם which demands that a Succah be constructed with enough walls to prevent rain being blown in from the sides. Rashi seems to understand that only within the latter opinion of Rav Masnah can we prove that according to R. Shimon a Succha is a דירת קבע. According to the opinion that learns that we need 4 walls from the words סוכת סוכת סוכות, it is more of a technicality, but according to Rav Masnah it is a requirement in the structure and construction of the Succah that the walls help prevent rain from entering. Only according to Rav Masna who considers the requirement of 4 walls to be a structural requirement can we prove that he holds of Diras Kevah.

Another opinion that is part of this list is the opinion of R. Yehuda who holds that a Succah can be built higher than 20 amos. Although the gemara 2a had many approaches to explain the opinion of Rav Yehuda, the gemara seems to consider the approach of Rava to be the primary approach, that we require a diras keva. Tosafos points out that even the opinions who disagree with Rava earlier would still maintain that according to R. Yehuda we need a diras keva, otherwise Abaye who rejects Rava earlier, should not be counting R. Yehuda as one of the opinions who demand diras keva. However, there is another problem with making R. Yehuda part of this list. The list is of those who demand that the Succah MUST be made in a particular way that has properties of a house - דירת קבע. Rav Yehuda doesn't seem to make any demand. He would certainly permit a lower Succah and presumably one that is not built as a דירת קבע, so how can he be part of this list? Tosafos seems to struggle with this as well. Tosafos explains that although R. Yehuda doesn't demand that it be built above 20 amos, the only reason he would permit it to be built above 20 amos is because he is assuming that no matter how high it is built, it is going to be built as a more permanent and fixed structure. Since despite the height it will be build in a permanent fashion, R. Yehuda holds that it makes no difference how high or low it is built. But had he held that it need not be build as a דירת קבע, he would not permit it to be above 20 amos.

Finally, Tosafos points out that the gemara in Yoma 10a assumes that if succah is a דירת קבע, then it would oblige a mezuza. Based on this Tosafos is forced to say that when R. Meir exempts the outer succah of the pottery maker from mezuza (8b), that is only the rest of the year, but during succos where he requires a diras keva he would also require a mezuza. This concept seems very different from the list of opinions who require diras keva. All the opinions who require a diras keva are saying that the succah must be built in a specific way, but what does this have to do with requiring a mezuza? Tosafos seems to understand that the diras keva has two applications, one is how the succah is built, the second is the status that the succah assumes after it is built. Any opinion who holds that the succah must be constructed as a diras keva, will also hold that after being built it will assume a halachic status of דירת קבע requiring a mezuzah.

We pasken that succha is a דירת עראי and therefore would not oblige a mezuzah. There is a machlokes whether just as holding that succah is a diras keva would necessitate a mezuza on a place that would otherwise be exempet, so too holding that succah is a דירת עראי would exempt from mezuza a place that would otherwise be obligated. The Pri Megadim (cited in MB end of 626) that by having status of a Succah it is automatically exempt from mezuza because the status of דירת עראי exempts it. Rav Moshe (O.C. 5:40:1) disagrees and holds that any place that would necessitate a mezuza the rest of the year would also be obligated in a mezuza on succos. The point of argument would hinge on how to learn the gemaras question and answer on 8b regarding the סוכת היוצרים that asks - ואמאי, תהוי חיצונה כבית שער הפנימית ותתחייב במזוזה, and answers משום דלא קביע. If it is speaking about during Succos and assuming דירת עראי, it would support Rav Moshe, but Tosafos who interprets that it is speaking about the rest of the year and not during succos, there is no proof from there whether דירת עראי exempts or doesn't exempt from succah.

Succah 3b - Mezuza on a Small House

The Braisa says that a house that is less than 4x4 Amos is patur from Mezuzah among other things that a small house doesn't qualify for. The gemara says that although to connect 2 cities by being with 70 2/3 Amos even בורגנין which are little huts used for a night work to connect the two cities, a house less than 4 amos does not. The gemara explains הני חזי למילתייהו והני לא חזי למילתיה, the huts are completely functional for what they are meant for, whereas a house that is less than 4x4 is unfit for what it is meant for. The Rashash claims that this supports the opinion of the Chamudei Daniel in Hilchos Mezuza cited by the Pischei Teshuva who says that a בית שער that is less than 4x4 requires a mezuza since it is completely usable and functional for what it is meant to be used for. The Chamudei Daniel holds that only areas that are meant to have the full function of a room must be at least 4x4 amos to be obligated in mezuza, but rooms that have a specific use that does not demand those dimensions are obligated in mezuza regardless. The Rashash considers the gemara to be a proof to the chamudei daniel.

In my opinion there is no proof at all from this gemara to support the approach of the chamudei daniel. Within the list of items in the braisa that demand the house to be 4x4 amos, there are two sections. All the d'oraysa mitzvos such as mezuza, ma'akeh, tzara'as, returning from battle and redemption in a walled city are based on the technicality that the Torah uses the term בית, and less that 4x4 doesn't meet the technical definition of a בית. The other Halachos that are Eiruvin related are not contingent on the technicality of being called a בית, rather on the functionality of a בית דירה, and when it is less than 4x4 it isn't suitable for a בית דירה. Within the second group the gemara makes a distinction between a house and a hut in that a hut is fit for its purpose even when it is small. This sevara helps to give the hut which doesn't serve as a full בית דירה to nonetheless qualify as being suitable as a בית דירה. However, halachos that are contingent on the technicality of being called a בית, such as mezuza, even if they are suitable and functional, do not meet the standard definition of  a בית, and are therefore patur from mezuza.

Succah 2b - Hilni HaMalka

The gemara cites a braisa where the chachamim went to visit Hilni HaMalka and found her sitting in a Succah higher than 20 amos and didn't say anything to her.  Rav Yehuda uses this as a proof that a Succah higher than 20 amos is still kasher. Although a woman is patur from Succah so there is no proof from their allowing her to remain in such a succah, the gemara says that since she had 7 sons which must include children above the age of chinuch, she would have followed the chachamim who told her to ensure that the Succah was kasher for them. Rav Yehuda therefore concludes that their silence indicates that they considered it to be a kasher succah.

There is a discussion in Tosafos Eiruvin 96a whether a woman who does a מצות עשה שהזמן גרמא is in violation of ba'al tosif. The Maharatz Chiyus points out that our gemara should prove that it is not a violation of ba'al tosif, otherwise Hilni HaMalka should not have been allowed to sit in a Succah. The Maharatz Chiyus explains that perhaps the opinion of the Rabbonon was that since the Succah was indeed passul above 20 amos, they allowed her to remain in it without a concern of ba'al tosif.

There is a major machlokes between the Rambam and Tosafos (Kiddushin, Rosh Hashana) which develops into a machlokes between the Mechaber and Rama (hilchos tzitzis) whether women can make a bracha on מצות עשה שהזמן גרמא. Although we don't consider it ba'al tosif, and consider it to be a kiyum mitzvah, the mechaber holds that it is not a sufficient level of mitzvah to warrant a bracha, whereas Tosafos and Rama hold that it is a mitzvah that warrants a bracha. According to Tosafos and the Rama it should follow that Hilni HaMalka was likely making a Bracha on the Succah, therefore even if the Rabbonon held that she and her children didn't need a kasher succah, they should have said something to her to prevent her from making a bracha l'vatala? The fact that the Rabbonon justify not mentioning that the Succah was passul because she was exempt from the mitzvah implies that she wasn't making a bracha, which supports the opinion of the Mechaber and Rambam.

I once visited a single older woman on Succos and realized that her succah that she was very proud of was completely passul. I was considering whether or not to tell her. This gemara seems to support the idea that it is unnecessary to say anything. Fortunately she was a sefardi woman who didn't make brachos on mitzvos. Had she been making a bracha on the Succah, I am not sure if there would be justification to remain silent.

Yoma 78b - Feeding Issurei D'rabonon to Children

The Shulchan Aruch writes in Hilchos Shabbos (343) that it is forbidden for an adult to "feed" something which is forbidden either by the Torah or M'drabonon, to a child. This concept is not based on the mitzvah of chinuch, but is rather based on a specific prohibition of לא תאכילם, from which the gemara learns out in Yevamos 114a - להזהיר גדולים על הקטנים. The Rashba cited by the Biur Halacha (quoting R. Akiva Eiger) disagrees and holds that if it is only an issur d'rabonon and being done for the sake of the child, not for the sake of the adult, it is permitted.

There is a major machlokes Rishonim addressed by Tosafos 77a, and by the Ran and Tosafos Yeshanim at the beginning of the perek whether the other inuyim (aside from eating and drinking) are forbidden by the Torah, or only m'drabonon. Rashi 74a d.h. shabason, seems to hold that they are only assur m'drabonon because Rashi equates the d'rabonons of Shabbos for which "Shabbason" is used as an esmachta, to these inuyim for which shabbason is also used as an esmachta. Yet, when explaining our gemara which says that one cannot put shoes on children because people will say אינשי עבדו ליה - an adult did it for him, Rashi writes that the Torah forbids an adult from feeding an issur to a child. Therefore, if we allow children to wear shoes, people will assume that an adult violated this prohibition by putting the shoes on the feet of the child. Even though Rashi holds that these inuyim are only M'drabonon, and even though it is being done for the sake of the child, Rashi assumes that there would be a violation of לא תאכילם - להזהיר הגדולים על הקטנים. This seems to be against the Rashba and is a support for the Shulchan Aruch who holds that even for an issur d'rabonon done for the sake of the child, we don't allow an adult to be the direct cause of it.

Yoma 77a - Smearing Non-kosher Fats On One's Skin

Someone asked me not long ago whether it is permitted to smear on one's skin items that are not kosher. This person in particular is very health conscious and is trying to figure out creative ways of absorbing certain items that they believe to be healthy into their body without violating any issurim. The question is, when the gemara makes the claim that סיכה כשתיה, how seriously do we take that? Do we view smearing oneself with something to be tantamount to drinking it? There is no question that in the context of Yom Kippur, the gemara clearly does. In the context of one who is forbidden to eat teruma using it to on their body is also explicit in the gemara Nidah 32a that it is prohibited. It is also obvious that issurei hana'ah one cannot use at all, therefore one could certainly not use Orlah which is assur b'hana'ah (as the gemara says in Pesachim 25b). The question is whether one can use other forms of forbidden foods to smear themselves with.

Tosafos 77a d.h. d'nan writes in the name of Rabbeinu Tam that aside from eating and drinking all the עינויים of Yom Kippur are only d'rabonon. Tosafos continues that the Rabbonon were only gozer that סיכה כשתיה by Yom Kippur and for Teruman, but nowhere else. Clearly Rabbeinu Tam holds that it is perfectly permissible to use all forms of ma'achalos ha'asuros and rub it on one's skin, so long as they don't ingest it. However, it seems from Tosafos that this approach is predicated on the assumption that the concept of סיכה כשתיה even where it does apply (Yom Kippur and Teruma) is only d'rabonon. However, if we assume that the עינויים of Yom Kippur are d'oraysa, as the Ran quotes from the Rambam, the concept of סיכה כשתיה must be d'oraysa at least in the context of Yom Kippur. Similarly, the Rambam (Terumos 10,2) implies that eating, drinking and anointing are all forbidden forms of using teruma (for one who may not use teruma), and that they are all the same, meaning that they are d'oraysa.

The question becomes, according to the Rambam who holds that the concept of סיכה כשתיה is d'oraysa, how does it apply to other issurim aside from Yom Kippur and Teruma. Do we assume that it is only d'oraysa in those two places, or are we to learn from there that it is always d'oraysa? And even if it is only d'oraysa in those two places, is it at least an issur d'rabonon elsewhere or is it completely mutar?
Even within the opinion of the Rambam that סיכה כשתיה is d'oraysa by Terumah and Yom Kippur, the Machane Ephraim (hearos at end of sefer - pg. מא in the old editions d.h. עוד בדין) writes that only a sicha done for the purpose of enjoyment would be d'oraysa, not if done for medicinal purposes. Therefore, the proof of Tosafos from Yoma 77b about one who has head injuries being able to do sicha is not a question on the Rambam because it is not for ta'anug, therefore only d'rabonon, and for refuah they weren't go'zer.

The Taz (Y.D. 117:4) cites the Beis Yosef quoting the Orchos Chaim that one may not anoint themselves with pig fat דסיכה בכלל שתיה היא. The Taz rejects that based on our Tosafos, and from the Rashba who permits anointing with pig fat, even when there is no sakana. However, The Taz concludes by citing the Issur V'heter that it is only permitted if there is some level of tza'ar, one who is perfectly healthy and is only using it as a moisturizer or for תענוג בעלמא, it may not be done. The Taz comments - וכן עיקר, implying that it can only be done to alleviate a tza'ar but cannot be done for just simple enjoyment.

It is very difficult to understand the hagdara of the Issur V'heter and Taz. If we say סיכה כשתיה is should be a regular issur, whether d'oraysa or d'rabonon, and should not be mutar to avoid tza'ar. The fact that it is mutar to avoid tza'ar implies that it is not a real issur, so why is it assur to use for pleasure?

The Nekudos Hakesef also quotes the same sources and seems to hold that Tosafos clearly permits it entirely, even for תענוג בעלמא, which is also the p'sak of the Bach. However, the Nekudas Hakesef comments that he saw those who are machmir not to wash with non-kosher soap, "and that is correct". He then continues to try and justify a minhag of not using pig fat in particular, while still using other forms of non-kosher fats.

In short, both the Taz and Nekudas Hakesef seem to conclude that it is technically permitted to use non-kosher items on one's skin, but one should preferably abstain from doing so for the sake of enjoyment. One should only use it if they NEED it. Similarly, the Aruch Hashulchan (29) justifies the practice of using soap from non-kosher items even for no particular need since it is already pagum, which implies that he agrees that otherwise it should not be used lichatchila. The Hagdara of the issur still needs explanation.
Perhaps the Issur V'heter holds that the distinction between תענוג and to alleviate צער is not a practical distinction of how necessary it is, Rather, he holds that the real issur of סיכה כשתיה is only when done for תענוג, as the Machaneh Ephraim says explicitly, but when done to avoid tza'ar, that does not qualify as ta'anug. Therefore, even other issurim outside of Y.K. and Teruma, we only permit it when it is to help alleviate tza'ar, but if it is done for ta'anug the Issur V'Heter is concerned for the opinion of the Rambam that it is d'oraysa on Y.K. and for Teruma, and therefore may apply to other issurim as well.
Regarding the issue of anointing oneself using items that are meant to be ingested, there is definitely not going to be an issur d'oraysa because the Rambam (Terumos 10:2 and 11:1) implies that even for Teruma we only say סיכה כשתיה if it is meant to be used in that way. If it is meant to be ingested, even the Rambam would hold that at worst it would be a d'rabonon. Being that we don't know what the Rambam would hold for other issurim outside of Terumah and Yom Kippur, and Tosafos is matir explicitly, one who feels that they need this item for their health can certainly be lenient to use it.

Yoma 70a - Rolling the Sefer Torah B'tzibur

The gemara explains that the first two parshiyos that were read by the kohen gadol, since they were in close proximity to one another, it can be rolled from achrei mos to emor. But the third parsha which was in parshas Pinchos could not be rolled to and therefore he must read it by heart. The gemara explains that rolling wasn't an option because it was a lack of kavod tzibbur, as rashi explains, having everyone sit silently until they reach the spot. The gemara explains that although generally we take out multiple sifrei torah, that is only when each sefer torah is read from by a different person so that there was no insult to the original sefer torah and no issue of causing an extra bracha (since each person is going to anyway make their own bracha), but this was not an option for the Kohein Gadol's reading (it would be a problem of p'gam and causing an unnecessary bracha).

The Tosafos Yeshanim points out that although reading by heart is not a perfect solution because it is a violation of reading the written torah orally, it is the lesser of the two evils. The Tosafos Yeshanim (in first answer) understands that the issue of reading written Torah by heart is only a מצוה מן המובחר, and is therefore trumped by kavod tzibbur.

It would seem from the gemara that on a shabbos rosh chodesh where we need to read from two separate places, we take out two sifrei torah rather than roll. If there is only one sefer Torah, it would be better for one to read the second section by heart rather than rolling the Torah and causing the tzibbur to wait. However, this is clearly not the minhag.

The Beis Yosef (144) writes that the hagahos mordechai and Ritva both say that it is better to disregard the kavod tzibbur, rather than disregard the takanas chachamim to read the inyana d'yoma of rosh chodesh (or 4 parshiyos). It is unclear how they would work this into the gemara which seems to say the opposite. Perhaps they would say that in the time of the gemara it wasn't set as an absolute takana to read the korbanos of mussaf from a sefer torah, but once it has become the overwhelming custom, it is like a takanas chachamim that overrides kavod hatzibbur.

The Rashba in a teshuva cited in the beis yosef was asked about the possibility of reading the second section from a chumash when there is only one sefer torah, rather than rolling. The Rashba answers and proves from our gemara that it is better to read from a chumash rather than roll, because even reading by heart is better than rolling. Clearly, the Rashba holds that reading from a chumash which avoids both the kavod tzibbur problem and the issue of reading the written torah by heart, is the best solution.

Yet, the Shulchan Aruch paskens like the Ritva that we roll rather than read from a chumash, and the Darkei Moshe agrees. The Magen Avrohom (7) asks this question on the Shulchan Aruch, that the gemara itself says that even if there is no alternative but to read by heart, we prefer that to the rolling of the Torah b'tzibbur. How does the pesak of the Shulchan Aruch fit with the gemara (The Magen Avrohom is apparently not content with saying that it only developed into a "takana" to read that section b'tzibbur, after the time of the gemara)? The Magen Avrohom writes that the concern of Kavod Tzibbur was only in the large group that was in the ezras nashim to hear the Kohein Gadol read from the Torah, it doesn't apply to the small groups in shul because מסתמא מוחלין על כבודם כדי לקיים קריאת המפטיר דשבת ור"ח ומפטיר דיו"ט דהוא תקנת הגאונים. The Magen Avrohom seems to hold that the takana alone wouldn't trump kavod tzibbur, but since there was a takana to read the inyana d'yoma from the sefer torah, we assume the tzibbur would be mochel on their honor.

The Nesiv Chaim (gilyon of shulchan aruch) explains the position of the hagahos mordechai. In the time of the gemara where the one getting the aliya read from the Torah it was impossible for the section to be read by heart because no one knew who would get that aliya (it was only possible for the kohen gadol who knew that he would be reading it to memorize it in advance). Since that was not a solution, the custom became to roll the torah b'tzibbur, which carries over into nowadays when there is a ba'al korei who can technically prepare it in advance since we also have a shortage of people who can read it by heart. Being that it became impossible to sustain the reading of the parsha by heart, the tzibbur is mochel on their kavod to allow the rolling. The difficulty with this approach is that it can still be read from chumashim as the Rashba suggests.

The Pri Chadash actually writes that the Shulchan Aruch following the Ritva and Hagahos Mordechai on only allowing the rolling since we can assume the tzibbur is mochel. They are not suggesting that it is a better solution to just reading from a chumash. Therefore he writes that if they want to read from a chumash rather than rolling the sefer torah, they can certainly do that.

A simple answer would have been that reading from a chumash is more of a lack of kavod tzibbur than rolling, therefore we roll rather than read from a chumash. The Pri Megadim rejects this answer because the reading from a chumash is only a lack of kavod tzibbur because they don't have a Torah (so we don't allow them to read from a chumash to make them feel bad and purchase a Torah - Beis Yosef 143), but in this case where there is a sefer torah, there is no lack of kavod tzibbur to allow the second reading to be done from a chumash.

Yoma 69a - Benefiting from Bigdei Kehuna

The gemara concludes that when one is already wearing bigdei kehuna to do the avoda, they can continue to wear it even after the time of the avoda - מפני שבגדי כהונה נתנו ליהנות בהן. But, the braisa says that the kohein wearing bigdei kehuna must remain in the beis hamikdash and not go out to the "medinah". Rashi explians that it would be a problem of treating the bigdei kehuna as non-kodesh garments. The language of Rashi implies that the nature of this prohibition would only be d'rabonon. Tosafos points out that just as one cannot go out l'mdinah wearing the bigdei kehuna, it would also be forbidden to put on the bigdei kehuna when one is not putting them on for the purpose of doing the avoda. The leniency is only to continue wearing them once they are on, but not to actually put them on. Tosafos understands this from the gemara in kiddushin which justifies the practice of wearing them after the time of the avoda as לא ניתנה תורה למלאכי השרת which implies that since it is unavoidable, it is permitted, but to put them on is certainly avoidable and not permitted (According to Tosafos perhaps one cannot wear them for much time after the avodah either because that is also easily avoidable).

The Mishna gives an option of reading the parsha either in the bigdei lavan that the kohein gadol was wearing until now, or to change into special clothing that was made for this purpose. The Tosafos Yeshanim points out that it does not offer the option of changing into the bigdei zahav to read the parasha. Perhaps the rationale is based on what Tosafos points out that he cannot lichatchila put on bigdei kehuna when unnecessary.

Tosafos adds an additional chiddush. Tosafos explains that the tzitz was an exception to the other bigdei kehuna because there is an explicit pasuk permitting it to be worn "always" - והיה על מצחו תמיד. This implies that the issur of putting on bigdei kehuna unnecessarily is not merely a d'rabonon violation (as rashi explains for walking out l'medina), but rather a Torah violation which is only waived by the Torah itself for the tzitz. Perhaps Tosafos will hold that just as placing on the bigdei kehuna not at the time of avoda is a Torah violation, the continuing to wear too long after the avoda where there is no justification of  לא ניתנה תורה למלאכי השרת, would also be a Torah violation. And perhaps Tosafos will hold that even walking out l'medinah would be a Torah violation, against Rashi who writes - שנוהג בה דרך חול, which implies that it is only a drabonon violation.

There is another point that is apparent from Rashi at the beginning of th sugya. The entire discussion is whether one is allowed to benefit from bigdei kehuna שלא בשעת עבודה, but it seems to take for granted that it is perfectly permissible to benefit from them and enjoy their warmth while doing the avoda. There doesn't seem to be any requirement to avoid the intention of pleasure that is being derived by the clothing that he is wearing while doing the avoda. Although when it comes to the concept of מצות לאו ליהנות ניתנו, the Ran (and most rishonim) holds that one cannot derive a hana'as ha'guf that is simultaneous with the mitzvah, this seems to be different. The bigdei Kehuna seem to be similar to a succah, where although there is an issur d'oraysa to benefit from a succah (learned from chagiga - succah 9a), one can enjoy the shade and protection of the succah while sitting in it for the mitzvah. The rationale is that the definition of succah is to be a protection from the elements, as the definition of clothes is to provide warmth, therefore we assume that these benefits that are simultaneous with the mitzvah are permitted.

Yoma 54a - A goy Making Tzuros for a Jew

The gemara says that there were tzuros of keruvim that were painted and carved into the wall of the beis hamikdash which were there even in the second beis hamikdash, after the keruvim on the Aron and the keruvim of Shlomo that stood on the floor were no longer present.

Tosafos launches into a discussion as to how there can be animal pictures printed in the machzorim. Although Tosafos begins by saying that pictures in siddurim and machzorim serve as a distraction so they are not a good thing, it is nonetheless permitted. Tosafos begins by saying we find that Rabban Gamliel had tzuros of the moon that he would show to the witnesses who came to testify about rosh chodesh, and the gemara says that although they are forbidden to make, "others made it for him". Meaning, it was done by goyim. Although the gemara says that it would still be forbidden to own and maintain, due to chashad (Rabban Gamliel was an exception since there were always people there so there was no chashad), Tosafos explains that since the pictures in the machzorim are not 3 dimensional, there is no chashad. There are 3 stages in Tosafos. In stage one the implication is that it would be forbidden for a Jew to make these tzuros in the machzorim, and it was only permitted to be maintained since it was not 3 dimensional. In the second stage Tosafos proceeds to explain that since they are not 3 dimensional, it is even permitted for a Jew to actually make pictures of these animals. In the final stage Tosafos explains that since the pictures were of animals, not of human faces, there is no prohibition whatsoever even to make 3 dimensional pictures.

R. Akiva Eiger, in the Gilyon HaShas asks that according to the first stage of Tosafos where it was forbidden for a Jew to make, but permitted because it was made by goyim, there should be an issur of amirah l'nachri? The Tosafos in Rosh Hashana explains that the only reason that Rabban Gamliel was able to have them made by goyim was because it was for a mitzvah purpose, implying that without that advantage it would be an issur d'rbonon of amirah l'nachri. Why then would it be permitted here to have a goy do it?

In truth the placement of R. Akiva Eiger's question is difficult. At the end of Tosafos because the distinction at the beginning of Tosafos is only a hava amina before Tosafos develops that there is no issur at all. In the end of Tosafos they make a practical distinction between the mador elyon and mador tachton, whether they can be made by others. R. Akiva Eiger could have asked his question on what Tosafos actually concludes. The Rashash rejects the question of R. Akiva Eiger by saying that we are not dealing from the perspective of those making it, we are dealing from the perspective of once it was already done whether it can be maintained. It may be assur to commission a goy to make it, but once it is done there is no issur in purchasing the machzor and using it.

Yoma 46b - Hutra or Dechuya

http://hearos.blogspot.com/2013/11/yoma-6b-hutrah-and-dechuya.html

The Rambam writes that Shabbos is dechuya in a situation of pikuach nefesh. The Kesef Mishna says that his source is from tu'mah where we pasken it is dechuya and not hutra. The Maharatz Chiyus asks from our gemara. How does the kesef mishna assume that since tu'mah is only dechuya, therefore shabbos is also only dechuya? Our gemara makes an assumption that shabbos is hutra for the korban tamid, yet tu'mah is only dechuya. We see from here that although tu'mah is only dechuya, shabbos can be hutra, so how does the kesef mishna make the assumption that they should be the same?

In my opinion the kesef mishna is correct. The issue is not a shabbos vs. tu'mah issue, rather the reason our gemara assumes that shabbos is hutra for korban tamid is because the mitzvah of korban tamid is meant to be done on shabbos. The system was set up with the natural conflict and the resolution being to bring the korban tamid even on shabbos, therefore rendering it hutra. However, when the two events conflict by chance or by circumstance, then it is dechuya, not hutra. Therefore, tu'mah b'tzibur is only d'chuya. Shabbos in the place of pikuach nefesh is also only dechuya because it is just circumstances of someone being in a life threatening situation that creates the conflict. Therefore, it is legitimate to learn shabbos for pikuach nefesh from tu'mah, and not learn from shabbos for korban tamid.

Yoma 42a - Is a kattan a la'av bar da'as?

The gemara quotes a mishna in Parah where the Tana Kama and R. Yehuda argue who is kasher for the kiddush (mixing ash and water) of parah adumah. T.K. holds that a חרש שוטה וקטן cannot do it, but a woman can. R.Y. holds the exact opposite, a woman cannot, but a child can. Regarding the machlokes of whether a woman can do it, the gemara says that they argue whether ונתן is meant to exclude ונתנה. But regarding the machlokes of whether a child can do it, the gemara says that they argue whether we darshen ולקחו to be inclusive, and therefore forcing us to include a child. It is understandable that R. Yehuda would normally exclude חרש שוטה וקטן from everything, but here the pasuk forces an inclusion. But why does he just include a child and not a חרש ושוטה? Tosafos writes: והא דמכשיר טפי בקטן במחרש ושוטה, יש לומר משום דאתי לכלל דעת. Since a child will out grow his לאו בר דעת status, it is more logical to include a child, rather than including a חרש ושוטה who are permanently fixed in their לאו בר דעת status.

The Chazon Ish (Parah 11:11) points out that when we include a child, we are obviously only including a child who is of age to make rationale decisions and would objectively be considered a בר דעת if not for the Torah excluding him. A child who is so young that he is essentially a שוטה would certainly be passul even according to R. Yehuda both for kiddush of the ash and water, and for the sprinkling. The machlokes is only about a child who has some level of intellect that we would consider a בר דעת in general - אלא שגזירת מלך הוא שאין דעתו מספקת במצות התורה אם לא היכי דאתרבי.

From the Chazon Ish it sounds like the real distinction between a child and a חרש ושוטה is that the latter are essentially not בר דעת, whereas a child has achieved some level of da'as that requires a גזירת התורה to consider insufficient for mitzvos. Therefore, if we have a pasuk we apply it to include a child faster than applying it to include a חרש ושוטה.

To me it seems that this approach doesn't fit well in Tosafos. If the advantage of a קטן is that he actually has a higher level of intellect that a חרש ושוטה, why would Tosafos write that his advantage is that he is אתי לכלל דעת, meaning he will come to be a bar da'as, rather than writing that he is included because he is already a higher level intellect than a חרש ושוטה. To me it seems from Tosafos that we are speaking about a child who is no more rational than a חרש ושוטה, yet we include him for kiddush since he has the advantage that he will become a bar da'as. The sevara seems to be that although he is no better now, it is a מום עובר, a blemish that will pass in due time. Since we are forced to include someone from the extra pasuk, we include a child.

Furthermore, we find that for other things we categorize a חרש together with a קטן and only consider a שוטה  to be a real לאו בר דעת. The halacha is that a child can make a kinyan when there is a דעת אחרת מקנה, someone else giving it to him. The Rambam (Mechira 29:4) implies that a shoteh cannot make a kinyan even with דעת אחרת מקנה - see magid mishna. The Ketzos (243:4) assumes that a חרש is like a child who can make a kinyan with a da'as acheres being makneh, it is only a shoteh who is a complete non-bar da'as who cannot. If the Chazon Ish were correct that the present intellect of the child is what makes him stand out, we should have included a חרש together with him since for kinyan we assume them to have the same level of intellect. The fact that we don't include a חרש for kiddush implies as Tosafos writes that the advantage of the child is not his present intellect, but rather that we regard his lack of intellect as a temporary problem.

Yoma 42a - Saying Bifanai Nichtav on a Gett

Rav Mendel Senderovic shlit"a has a letter printed in his sefer Atzei Besamim (38), that he sent to Rav Nota Greenblatt shlit"a asking what is the appropriate language for the shliach who brings a gett to use. The halacha demands that when a shliach delivers a gett outside of EY he must declare at the time of delivery - בפני נכתב ובפני נחתם, confirming that it was written and signed in his presence. However, what often happens is that the sofer ends up as the shliach, so the question becomes whether to stick with the precise nusach of בפני נכתב ובפני נחתם that was instituted by chazal, or modify the nusach to be אני כתבתיו ובפני נחתם which is more accurate. Rav Senderovic points out that it seems to be a dispute between the Radvaz and Panim Meiros. Rav Nota responded that his custom is to say the standard בפני נכתב ובפני נחתם then to deliver the gett into the hands of the woman, and immediately to say אני כתבתיו ובפני נחתם. 

I am also in this situation quite often where I am the sofer and the shliach. I do what Rav Nota suggested and what I have seen him do (However, I didn't notice that Rav Nota was careful to say אני כתבתיו ובפני נחתם specifically after the delivery, rather he says בפני נכתב ובפני נחתם אני כתבתיו ובפני נחתם as one continuous phrase and immediately places the gett into her hands, which is what I do as well.)

There is a strong proof from the gemara on todays Daf that the language of בפני implies that it was done in your presence, but that you weren't actually the one doing it, thereby demanding a modified language so that the testimony isn't false. The gemara says that the pasuk ושחט אותה לפניו by the para aduma implies שיהא זר שוחט ואלעזר רואה. Meaning, the fact that the Torah says that it is done in the presence of Elazar implies that it is NOT done by Elazar himself, and is used as a source that the shechita of the parah doesn't need a kohein. Similarly, the language of בפני נכתב would imply that it was written by someone else in the presence of the one saying those words, but not by the person himself. Therefore it would make sense that the phrase should be modified to clearly state that the shliach himself did the writing of the gett.