Shabbat 24

Today's shiur is sponsored by the Mitchell family of New York City in honor of the b'nai mitzvah of their twins, Aaron and Joshua, and by Rachel and Oren Seliger in memory of Reuven ben Yehuda and Devora z"l, Saba Reuven, who lived his life by Torah ve'avoda and was a founding member of Kibbutz Tirat Zvi. 

Does one mention of Chanuka in birkhat hamazon? If so, where and why there and not in the usual place for additions? Should one add mention of Rosh Chodesh in birkhat hamazon? It is the same as Chanuka or different - why? Does one mention Chanuka in mussaf on Shabbat? Does one mention Rosh Chodesh in the blessing for the haftorah if Rosh Chodesh falls on Shabbat? The gemara suggests various comparisons. The mishna raises different opinions about what oils one can or cannot use on Shabbat. Oil of truma that became impure cannot be used on Yom Tov because one cannot burn sanctified items on Yom Tov. From where is this derived? Four different answers are brought.