(a) The Tana rules that if someone meant to declare ...
1. ... something 'Terumah' and said by mistake 'Ma'aser' or vice-versa, 'Olah' and said by mistake 'Shelamim' or vice-versa - then his declaration is invalid, and the same applies to someone who meant to declare ...
2. ... that he will not enter room a., and said by mistake that he will not enter room b., or that he will not benefit from Reuven, and he said by mistake Shimon (see Tiferes Yisrael).
(b) He learns from the Pasuk in Ki Setzei "Motzei Sefasecha Tishmor ve'Asisa" and the Pasuk in Vayakhel "Kol N'div-Leiv" - that one's heart must conform with one's mouth (what one declares) for any of the above declarations to be valid (see Tosfos Rebbi Akiva Eiger).
(a) When the Mishnah validates the Terumos and Ma'asros that a Nochri or a Kuti have separated, it is referring to - to a Nochri who Ma'asered his own crops, and not those of a Yisrael (see Tosfos Yom-Tov).
(b) We learn from the Pasuk in Korach "Kein Tarimu Gam Atem" - that a Yisrael can only appoint a Sheli'ach who is a Jew like himself, but not a Nochri.
(c) The Tana rules that the Hekdesh of a Nochri - is valid too.
(a) Based on the assumption that the field of a Nochri is subject to Orlah (see Tosfos Yom-Tov), Rebbi Yehudah holds that it is not subject to Kerem Revai (see Tosfos Yom-Tov). The Chachamim hold - that it is.
(b) The Mishnah rules that the Terumah of a Nochri that fell into less that a hundred of Chulin - is Medama'as (and Asur for Zarim to eat.
(c) The Tana Kama also obligates a Zar who eats it to pay an extra 'fifth' - whereas Rebbi Shimon exempts him from doing so (see Tosfos Rebbi Akiva Eiger).