(a) A Kohen - is not permitted to feed his animals regular Terumah (because it is forbidden to feed animals food that is fit for a human.
(b) The Tana nevertheless permits him to feed them Karshinei Terumah (vetch, or horse-bean) - because it is basically animal food.
(c) It must nevertheless be fit for human consumption - otherwise, it would not be subject to Terumos and Ma'asros.
(a) The Mishnah - permits a Yisrael who hires a cow from a Kohen to feed it Karshinei Terumah (since it remains the Kohen's property [even though the Yisrael is obligated to feed it]).
(b) The Yisrael is permitted to use Terumah for that purpose (and it is not considered theft) - because if e wanted, he could have given the Karshinim to the Kohen directly, and now that he did not, we know that the Kohen will be only too pleased if he now feeds his animal with it instead.
(c) We learn that a Kohen who hired a cow from a Yisrael may not feed it Terumah from the Pasuk "ve'Kohen ki Yikneh Nefesh Kinyan Kaspo" - by extrapolating from it that he is not permitted to feed any soul (even that if an animal) that he has not acquired.
(a) The Mishnah now discusses the Din of 'ha'Sham Parah', which means - that Reuven receives a cow from Shimon that has just been assessed, to fatten. And after a given time, it is assessed again, at which point it is sold, and Reuven and Shimon divide the difference.
(b) The Tana ...
1. ... forbids a Yisrael who is 'Sham Parah' from a Kohen to feed it Terumah, but permits ...
2. ... a Kohen who is 'Sham Parah' from a Yisrael to do so ...
(c) ... because as opposed to the hirer - the person who is Sham acquires the animal.
(a) The Mishnah permits burning Shemen Sereifah - Terumah oil that because Tamei and that needs to be burned to light up Shuls, Batei Medrash and dark alleyways.
(b) One may one use it to illuminate the room for a sick person - provided there is a Kohen present who will benefit from it ...
(c) ... because of the S'vara 'Ner le'Echad, Ner le'Me'ah (a lamp for one is a lamp for a hundred)'.
(d) The Mishnah - permits a Yisrael to use Terumah-oil to illuminate a room for his daughter who married a Kohen.
(a) Rebbi Yehudah ...
1. ... forbids using Terumah-oil to illuminate the house of a mourner (even if there is a Kohen there) - because he is afraid that someone will carry the lamp to a room where there is no Kohen.
2. ... nevertheless permits using Terumah-oil to illuminate the house where a wedding-feast is taking place - because, since everyone is wearing his best clothes, he assumes that nobody will pick up the lamp and transfer it to another room.
(b) Rebbi Meir ...
1. ... forbids using Terumah-oil to illuminate the house where a wedding-feast is taking place (even if there is a Kohen there) - because he is afraid that, seeing as everyone there is in a good mood, someone is likely to move the lamp to another, but he ...
2. ... permits using Terumah-oil to illuminate the house of a mourner - because people who are feeling dejected are less likely to do so.
(c) Rebbi Meir adopts the Chumra of both opinions. Rebbi Shimon - adopts both leniencies ...
(d) And that is how we rule (see Tiferes Yisrael and Tos. Yom-Tov).
***** Hadran Alach 'Ein Nosnin', ve'Salik Maseches Terumos *****
On to Ma'asros