1)

(a)A Zar is Chayav to add a fifth (a Chomesh) - if he eats Terumah be'Shogeg (see Tos. R. Akiva Eiger).

(b)A Chomesh in real terms - is a quarter (a fifth of the total)

(c)Besides eating - the Tana incorporate in the ruling someone who drinks wine (see Tos. R. Akiva Eiger DH 've'Echad' and DH 'Echad') of Terumah and someone who anoints himself (or somebody else) with Terumah oil.

(d)We learn from the Pasuk "va'Tavo ka'Mayim be'Kirbi, u'che'Shemen be'Atzmosai" - that Sichah (anointing, that is rubbed into the bones) is equivalent to drinking (as far as Terumah goes).

2)

(a)The Zar pays the Chomesh irrespective whether he ate Terumah Tehorah or Terumah Temei'ah.

(b)When the Tana says Meshalem Chumsha ve'Chomesh Chumsha", he means - that if he subsequently eats the Chomesh, he is obligated to pay a Chomesh of that too.

(c)He actually pays the Kohen - Chulin that is fit to become Kodesh (that no longer contains any Terumos and Ma'asros).

(d)The reason for this might be because the Zar is not permitted to pay a debt with money that is not his (see Tosfos Rebbi Akiva Eiger and Tiferes Yisrael). In fact though, we learn it from the Pasuk "ve'Nasan la'Kohen es ha'Kodesh" - from we extrapolate 'Davar ha'Ra'uy Lihyos Kodesh'.

3)

(a)The Chulin that the Zar pays the Kohen ...

1. ... for the first Batch that he ate actually Terumah (see Tos. R. Akiva Eiger) and the same will apply ...

2. ... should he eat the batch that he gave the Kohen as payment as well.

(b)The Mishnah rules that if the Kohen is Mochel the Zar - his Mechilah is ineffective ...

(c)... because since the Torah requires him to pay something that is fit to become Kodesh (even if the Kohen would prefer money), it is clearly outside the Kohen's jurisdiction.

4)

(a)A Kohenes - is permitted to eat Terumah.

(b)The Mishnah rules, in a case where a bas Yisrael married a Kohen after having eaten Terumah ...

1. ... before having given it to a Kohen - that she may keep both the Keren and the Chomesh and eat them herself.

2. ... after having given it to a Kohen - that she must give the Keren to the owner, but that she may keep the Chomesh herself.

(c)She is permitted to keep the Chomesh herself - because the Zar has the option of giving it to whichever Kohen he chooses.

5)

(a)According to Rebbi Meir, if Reuven feeds his workers or his guests Terumah be'Shogeg, he is obligated to pay the Kohen the Keren - because one must pay for having stolen from Hekdesh.

(b)Yet they pay the Chomesh, and not he - because the Torah writes (in connection with Chomesh), "ve'Ish ki Yochal Kodesh ... ", confining the obligation to pay a Chomesh to someone who eats Terumah (to preclude destroying it in any other way).

(c)According to the Chachamim, they must pay the Keren as well - whereas Reuven pays them for the meal that he ought to have given them.

(d)In practical terms - according to Rebbi Meir, Reuven pays the (Kohen) the value of Terumah, whereas according to the Chachamim, he pays (the employers) the value of Chulin.

6)

(a)A Zar who stole Terumah but did not eat it, is obligated to pay the Kefel (for stealing) 'Dmei Terumah' - which means that he only needs to give the owner the value of Terumah (which is cheaper that of Chulin, since Kohanim are not permitted to eat it when they are Tamei).

(b)If he then ate it, he must pay - Keren plus a Chomesh Chulin (which must be paid in a commodity that can become Terumah) for eating it, and Keren ('Dmei Terumah' i.e. money, should he so wish]) for the Kefel (see Tosfos Yom-Tov).

(c)Whereas if he stole Terumas Hekdesh and ate it - he pays two times the Chomesh (for eating Terumah and for benefiting from Hekdesh [see Tos. Yom-Yov and TOS. R. Akiva Eiger]), but is exempt from paying double for stealing ...

(d)... because the Torah writes "Yeshalem Shenayim le'Re'ehu", which precludes Hekdesh.

7)

(a)Rebbi Meir disqualifies a Zar who is Chayav to pay the Kohen Chulin which is fit to become Terumah, from paying ...

1. ... Leket, Shikchah, Pe'ah or Hefker - because these are all not eligible to become Terumah or Ma'aser.

2. ... Ma'aser Rishon whose Terumah has been separated or Ma'aser Sheni or Hekdesh that were redeemed too (because initially, they were not fit to become Terumah, despite the fact that now, they are no different than Chulin that has been Ma'asered [see Tosfos Yom-Tov]).

(b)The Chachamim seem to argue only - on the last three cases Ma'aser Rishon she'Nitlah Terumaso and Ma'aser Sheni ve'Hekdesh she'Nifdu (see Tiferes Yisrael).

(c)The Halachah is - like the Chachamim.

8)

(a)According to Rebbi Eliezer, a Zar who is Chayav to pay the Kohen Chulin that is fit to become Terumah is permitted to pay with a different species (e.g. dates for having eaten Gerogros) - provided he pays good quality fruit (even if what he ate was inferior.

(b)Assuming the payment is 'L'fi Damim (according to the value), rather than 'L'fi Midah' (according to the measure, irrespective of the value) - this will mean that he is obligated to pay fruit that the Kohen will be able to sell easily (even though the value is the same anyway).

(c)Rebbi Akiva holds - that he has to pay the same species that he ate.

(d)Assuming the Zar ate, say, cucumbers of Terumah in Erev Shevi'is (which is one of the first species whose last year's stock is finished) - (where he can neither pay with another species [from last year's stock] nor can he pay with cucumbers from the Shemitah year [see Bartenura]), he will have to wait until the following year and with freshly-grown cucumbers.

9)

(a)Rebbi Eliezer Darshens the Pasuk "ve'Nasan la'Kohen es ha'Kodesh" to mean - that the Zar must pay with anything that is fir to be Terumah; whereas according to Rebbi Akiva, it means - that he must pay whatever species of Kodesh that he ate.