Ta'anis 28b - Hallel on Rosh Chodesh

A few seperate points:

1. Rashi explains that hallel on chanuka is "like d'oraysa". This can be understood based on chasam sofer (o.c. 208) that the parsumei nissah is a kiyum d'oraysa, just that chazal choose how it should be done for each yom tov (candles for chanuka, megilla for purim). Therefore, hallel on chanuka was instituted by the rabonon but is a kiyum d'oraysa and therefore can push off even tefillah d'orayasa such as mincha. Although even rambam holds tefillah everyday is only d'oraysa once a day so mincha should not be considered d'oraysa? Rashi explains 28a mincha is d'oraysa - since yitzchok instituted it, its like d'oraysa. Meaning that it is not a chiyuv d'oraysa, rather a kiyum d'oraysa. Therefore, the kiyum d'oraysa of hallel can push off the kiyum d'oraysa of tefillah of ma'mados (but zman atzei kohanim which is not even a kiyum d'oraysa can't push off mincha).

2. Tosafos (d.h. yom tov) says that the miracle of chanuka became greater everyday. This clearly assumes that the entire jar of oil was poured it on the first day, so that everyday it continued to burn it was a greater miracle. To the exclusion of one of the beis yosef's answers, that everyday they poured 1/8 of the jar.

3. Tosafos implies that full hallel must be said once over pesach but it is not specific to the first day. Therefore if one did not say full hallel on the first day, they can do so on any other day. However, on day 7 the poskim bring a midrash that full hallel should not be recited since the mitzrim drowned on that day. This reason is only necessary for a situation where one did not say full hallel until the 7th day, so they should really say it on day 7 - to that the poskim say it should not be recited since the mitzrim drowned that day.