The expertise of Kutim in practicing Mitzvot which they accepted: Gittin 10a
Whichever Mitzvah the Kutim decide to keep, they keep better than regular Jews: Gittin 10a
Whether the Kutim kept Shabbat: Nedarim 31a
Whether the Kutim kept the Mitzvah of the husband to have sexual relations with his wife on Friday night: Nedarim 31a
Whether the Kutim kept the Mitzvah of ascending to Jerusalem for holidays: Nedarim 31a
History of the Kutim
The Kutim appealing to Alexander Mokdon to destroy the Second Temple: Yoma 69a
The Kuti attempted to light fake torches to throw off the Publication of New Month: Rosh HaShanah 22b
Kuti idolatry: Taanit 5a-b
Interacting with Kutim
Saving the Life of a Kuti on Shabbat: Yoma 85a
Looking at a Kuti: Megillah 28a
Creating a partnership with a Kuti: Megillah 28a
Punishment for causing a Kuti to have a wound which does not inflict so much as a Perutah of damage: Makkot 8b-9a
Stories of Kutim
How two kutim handled the breakup of a manager/investor partnership, and Rav Pappa's rulings for them: Bava Metzia 69a-b