(Beraisa): Everyone is believed to say that a place was checked, even women and slaves.

(Rebbi Yirmeyah): Women are not included as they are not able to check themselves since they are sluggish and do not check thoroughly. (Note: This statement follows the girsa of Tosefos in Bavli Eiruvin 59a, as brought by Rav Chaim Kanievski).

Kusim (Nochrim whom Sancheriv settled in place of the exiled 10 Shevatim - lions were eating them, so they converted, but they did not keep many of the Mitzvos) - if they make matzos with the Jews, they are even believed about destroying the Chametz. If not, they are not believed.

(Rebbi Yosa): They are only believed about a house but not about a courtyard (the prohibition of owning Chametz in one's home is explicit in the pasuk, which is not the case for owning Chametz in one's courtyard) - they expounded the pasuk "...it shall not be found in your houses'' - but in your courtyards it may be found.

(Beraisa - Raban Shimon ben Gamliel): Any mitzvah that the Kusim keep, they are even more particular about it than the Jews.

(Rebbi Shimon): This was only true when they lived in isolation in their villages but now that they live together with other nations, they have no mitzvos at all and are completely untrustworthy.

(Beraisa - Rabanan): One teaches the laws of Pesach on Pesach, the laws of Shavu'os on Shavu'os and the laws of Succos on Succos. But in the Beis Hamedrash, they ask about the laws 30 days before the festival. Raban Shimon ben Gamliel says 2 weeks before.

Rebbi Yochanan follows the Rabanan and his colleagues follow Raban Shimon ben Gamliel-

Rebbi Yochanan explained that the Rabanan's reasoning was that Moshe taught about Pesach Sheni on Pesach Rishon (which was 30 days before)

Chevraya (Sages) explained that RSBG's reasoning was that Moshe taught the laws of Pesach on Rosh Chodesh Nisan (which was 2 weeks before).