Beitzah 21: A Non-Jewish Army in a Jewish Town

The case of an animal that is jointly owned by a Jew and a non-Jew, is it permissible to slaughter that animal on yom tov (for yom tov)? And how does that relate to the discussion about animals that are nedavot - gifts to the kohen? Plus, the case of an ancient Jewish twin that has a non-Jewish army garrisoned there, relying on certain aspects of Jewish labor - but what about on yom tov? Also, a couple of new mishnayot towards the end of the daf: what about heating water for washing on yom tov? And: Rabban Gamliel on Beit Shammai's stringencies (when he accepts them).