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.