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1)

(a) We have just concluded a series of six Mishnahs that all teach us 'ha'Peh she'Asar Hu ha'Peh she'Hitir'. We would not know the case of ...

1. ... 'ha'Eidim she'Amru K'sav Yadeinu Hu Zeh' from that of 'u'Modeh Rebbi Yehoshua be'Omer la'Chaveiro Sadeh Zu shel Avicha Haysah' - because there is no loss of pocket in the former case (like there is in the latter), and it is the loss of pocket to which we would have attributed 'ha'Peh she'Asar' (because a person would not say 'shel Avicha Haysah' [implying that the field was not his] unless he wanted to add 'u'Lekachtihah Mimenu').
2. ... 'u'Modeh Rebbi Yehoshua be'Omer la'Chaveiro Sadeh Zu shel Avicha Haysah' from that of 'ha'Eidim she'Amru K'sav Yadeinu Hu Zeh' - because it is in the latter case that he would not retract, because he is speaking on somebody else's behalf, whereas in the former case, where his statement is made on his own behalf, we would suspect him of changing his mind in the middle (for his own benefit.
3. ... 'Eishes Ish Ani u'Gerushah Ani' from the previous cases - because we cannot learn Isur from Mamon.

(b) We suggest that the Tana needs to insert the case of 'Nishbeisi u'Tehorah Ani', because of the clause 've'Im mi'she'Niseis Ba'u Eidim, Harei Zu Lo Seitzei' - according to those who say that this clause refers to the Seifa only (because of the principle 'bi'Sh'vuyah Heikilu'). But according to those who maintain that it pertains to the Reisha too, we obviously cannot say that.

(c) So we conclude that the Tana needs to insert it because of the continuation 'Sh'tei Nashim she'Nishbu' - to teach us that we are not worried about 'Gomlin'.

(d) And the case of 'Sh'nei Anashim, Zeh Omer Kohen Ani ... ' needs to be added - because of the Machlokes between Rebbi Yehudah and the Rabbanan (whether Ma'alin li'Kehunah al-Pi Eid Echad' or not).

(a) If one witness testifies that both he and his friend are Kohanim, he is believed to feed him Terumah - but not to allow him to marry a Meyucheses (of pure stock - see Tosfos DH 'Aval').

(b) Rebbi Yehudah is more strict than the Tana Kama. According to him - one witness is not believed even to feed a man Terumah, and that there would have to be three men, in order to be believed, two witnesses for each one. We currently presume Rebbi Yehudah's reason to be because he is worried about 'Gomlin'.

(c) In a Mishnah in D'mai, the Tana Kama holds that if two ass-drivers arrive in town, each one claiming that his produce is new or that it has not been Ma'asered, but that his friend's is old (and therefore better) and has been Ma'asered, he is not believed, because we suspect 'Gomlin' (an agreement by which he will testify about his friend's produce in one place, and his friend will testify about his in the next).

(d) Rebbi Yehudah says - that he is believed (despite the suspicion of 'Gomlin'). We see from here that Rebbi Yehudah does not hold of 'Gomlin'.

(a) To resolve the apparent discrepancy between Rebbi Yehudah in this latter Beraisa, and Rebbi Yehudah in the former one (where he forbids the 'Kohen' to marry a Meyucheses - of pure stock), Rav Ada bar Ahavah Amar Rav inverts the opinions in the latter Beraisa (so that Rebbi Yehudah suspects 'Gomlin', and the Rabbanan don't). Abaye resolves the fact that Rebbi Yehudah is stringent in the Beraisa regarding the Kohen, but lenient in the Beraisa regarding D'mai without inverting the opinions - by applying the principle 'bi'D'mai Heikilu' (a principle that is widely applicable, because the institution of D'mai is a de'Rabbanan which is built on a minority of Amei ha'aretz who do not Ma'aser).

(b) But that only resolves the discrepancy in Rebbi Yehudah. Rava resolves the discrepancy in the Rabbanan, by establishing the latter Beraisa (where the Rabbanan are stringent) like Rav Chama bar Ukva - who establishes another Beraisa when the person concerned is seen in possession of selling implements, indicating that he intends to sell his produce. This conveys the impression that he intends to sell it, and increases the likelihood of 'Gomlin', and explains the Rabbanan's stringent view.

4)

(a) Rav Chama bar Ukva was referring to a Beraisa which cited the case of a case of a potter who left his jars unguarded and went to the river for a drink. The status of the potter - was that of a Chaver.

(b) Rav Chama bar Ukva explains the Beraisa which rules 'Eilu ve'Eilu Temei'os - when the potter has his selling-implements on hand, indicating that he intents to sell, and so everyone comes to examine his produce; whereas the Beraisa which rules 'Eilu ve'Eilu Tehoros' - speaks when he does not have his selling-implements on hand, so that people are discouraged from coming to examine the crops for sale.

(c) A Mishnah in Taharos concludes that the inner pots are Tahor, and the outer ones Tamei. Rav Chama bar Ukva establishes it when he does not have his selling-implements on hand, but that the crops are placed at the side of a road beside 'Chifufi' (stone or wooden posts placed at close, regular intervals, to prevent the wagons from damaging the walls). These posts, together with his crops, make the road narrower, forcing the people to rub against the outside of his crops as they pass.

(d) Alternatively, Rebbi Yehudah and the Rabbanan (in the Beraisa - whether two witnesses who each testify that his friend is a Kohen, is believed to feed him Terumah or not), are not arguing over 'Gomlin' at all. The basis of their dispute is - whether Ma'alin mi'Terumah le'Yuchsin (we instate a Kohen from Terumah to Yuchsin) or not. Rebbi Yehudah holds that one may (therefore one cannot believe the friend with regard to Terumah either), the Tana Kama holds that one may not (in which case one believed him with regard to Terumah).

(a) We ask a She'eilah whether one can attest to a Kohen's lineage from a document. The She'eilah cannot be with regard to a document where the witness signs his name as so-and-so the Kohen - because in that case, it is only he himself who is attesting that he is a Kohen.

(b) The case must therefore be - when two witnesses signed a document, in which the debtor wrote that he, so-and-so the Kohen, borrowed money ... , which the witnesses signed.

(c) Rav Huna and Rav Chisda argue over this point. Their dispute is based on whether the witnesses attest just to the loan, or whether they attest to everything in the Sh'tar, even the details pertaining to the characters involved.

1. ... hold 'Ein Ma'alin mi'Duchan le'Yuchsin', even if we hold 'Ma'alin mi'Terumah le'Yuchsin' - because if a Zar eats Terumah he is Chayav Misah, whereas if he Duchens, he has only transgressed the Asei of "Koh Sevarchu".
2. ... hold 'Ma'alin mi'Duchan le'Yuchsin', even if we hold 'Ein Ma'alin mi'Terumah le'Yuchsin' - because, whereas eating Terumah is something that is normally done discreetly, Duchening is done publicly, and a Zar would not have the Chutzpah to Duchen in public if he was not a Kohen.

(a) Rav Chisda and Rav Avina argue over this She'eilah (whether 'Ma'alin mi'Duchan le'Yuchsin' or not). When Rav Nachman bar Yitzchak posed this same She'eilah to Rava, he quoted a Pasuk in Ezra. The problem with the Kohanim there was - that many of them (no less than the Yisre'eilim) had intermarried with Nochrim, and their children were Chalalim (see Rashash).

(b) When the sons of Barzilai ha'Gil'adi were unable to find documentation to prove their pure lineage - Hatirshasa (alias Nechemyah) ruled that they were permitted to continue eating Terumah, because that is what they had been doing in Bavel (where they had been eating Terumah de'Rabbanan), but not Kodshei ha'Mikdash.

(c) When he said " ... ad Amod Kohen le'Urim ve'Tumim" - he meant until Mashi'ach comes, because the Urim ve'Tumim was not reinstated in the time of the second Beis-Hamikdash (which was being built at that time).

(d) Rebbi Yossi is the one to cite this episode from Ezra. He extrapolated from there - the principle of 'Gedolah Chazakah'.

(a) Despite the fact that the sons of Barzilai ha'Gil'adi would be able to continue Duchening, this is not a proof that 'Ein Ma'alin mi'Duchan le'Yuchsin' - because their Chazakah had been weakened by the fact that everybody could see all the Kohanim eating Kodshim except them.

(b) We prove this answer from the fact that Ezra permitted them to eat Terumah. If not for what we just said - how will those who hold 'Ma'alin mi'Terumah le'Yuchsin' explain that?

(c) The significance of 'Gedolah Chazakah' (according to the first answer) - is that whereas before they only ate Terumah de'Rabbanan, Hatirshasa now permitted them to eat Terumah d'Oraysa (although this in itself, is difficult to understand).