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1)
(a) The Beraisa ...
1. ... permits separating Terumah from Te'einim on to G'rogros wherever it is common to make G'rogros from Te'einim.
2. ... forbids separating Terumah from G'rogros on to Te'einim even if it is common to make G'rogros from Te'einim.
(b) The Reisha cannot be speaking in a case where there is a Kohen to whom to give it, due to a Mishnah in Terumos, which rules - that wherever there is a Kohen, it is better to give the superior quality commodity (and figs are superior to dried-figs).
(c) The problem with the Seifa is then - why one does then give G'rogros, since the Mishnah there rules that wherever there is no Kohen, it is better to give the commodity that lasts longer (and dried-figs last longer than fresh ones).
(d) We reconcile the Reisha with the Seifa - by establishing the former where there are no Kohanim, and the seifa, where there are.

2)
(a) We might have resolved the discrepancy - by turning the Beraisa and the Mishnah into a Machlokes Tana'im.
(b) Rav Papa therefore extrapolates from there - that it is preferable to establish two Mishnahs/Beraisos in two different cases, than to turn it into a Machokes Tana'im.

3)
(a) We already discussed our Mishnah 'Kol ha'Menachos Niloshos be'Poshrin u'Meshamran she'Lo Yachmitzu'. The Tana rules that someone who kneads, shapes or bakes the Minchah as Chametz, after the Kemitzah has been performed - transgresses a Lo Sa'aseh.
(b) The Tana quotes the Pasuk "Kol ha'Minchah Asher Takrivu la'Hashem Lo Sa'aseh Chametz" - pertaining to the Reisha of our Mishnah (which takes place before the Kemitzah).

4)
(a) Resh Lakish learns the Pasuk there "Lo Se'afeh Chametz, Chelkam" - that even the Cheilek of the Kohanim may not be baked as Chametz (the Seifa of our Mishnah).
(b) In spite of having already written "Lo Se'aseh Chametz", the Beraisa learns from "Lo Se'afeh Chametz" - that one is Chayav for the baking alone, or for just kneading or shaping it.
(c) We also include Kituf (smoothening the surface of the dough with water) in this D'rashah. We might have thought that one is not Chatav for performing Kituf alone - because it less of a Melachah than the others.
(d) Resh Lakish learns the above D'rashah (not from "Le Se'afeh Chametz", but) - from the juxtaposition of "Chelkam" to the Pasuk.

5)
(a) Despite Resh Lakish's D'rashah "(Lo Se'afeh Chametz, Chelkam"), the Tana knows to Darshen a second D'rashah from the same Pasuk (as we just explained) - because the Torah inverts the order, and writes "Lo Se'afeh Chametz, Chelkam", instead of "Chelkam Lo Se'afeh Chametz".
(b) The Tana includes all the other Melachos that we discussed - based on the principle 'Kol Davar she'Hayah bi'Chelal, Ve'yatza min ha'K'lal Lelamed, Lo Lelamed al Atzmo Yatza, Ela Lelamed al ha'K'lal Kulo Yatza'.
(c) We also ask why "Lo Se'aseh Chametz" is not a K'lal, and "Lo Se'afeh Chametz" a P'rat - in which case we would apply the principle 'Ein bi'Ch'lal Ela Mah she'bi'P'rat', and one would only be Chayav for baking the Minchah as Chametz (but not for the other Melachos).
(d) Rebbi Apturiki answers - with the principle that a K'lal and P'rat that are far apart, are not considered a 'K'lal u'P'rat', and here the K'lal is in Vayikra and the P'rat, in Tzav.

6)
(a) Rav Ada bar Ahavah (or Kadi) queries this from a Beraisa. The Torah writes by the Sa'ir Nasi "Ve'shachat Oso bi'Mekom Asher Yishachet es ha'Olah" - to teach us that Sa'ir Nachshon required Tzafon.
(b) We reconcile this with the Pasuk "bi'Mekom Asher Tishachet ha'Olah Tishachet ha'Chatas" (which seems to be teaching us the same thing) - by establishing the second Pasuk as a 'Binyan Av' to incorporate all Chata'os in the Din of Tzafon.
(c) Alternatively, we might learn from these two Pesukim (based on the former Pasuk) - that only the Sa'ir Nachshon requires Tzafon, but not other Chata'os.
(d) We conclude that the Pasuk "Ve'shachat es ha'Chatas bi'Mekom ha'Olah" - is a 'Binyan Av' to include all Chata'os in the Din of Tzafon.

7)
(a) However, were it not for the third Pasuk, we would have learned the first two Pesukim in the way that we explained. We think to correlate them - by turning them into a 'K'lal u'P'rat' (even though they are written far apart [a Kashya on what we just learned]).
(b) Rav Ashi refutes this Kashya on the grounds that, even if the one was a P'rat and the other a K'lal, they could not possibly be considered a 'K'lal u'P'rat' - because the Pasuk 'Ve'shachat Oso' (by Sa'ir Nasi) is written first, in which case it would be a K'lal u'P'rat ...
(c) ... which would then include all Menachos in the Din of Tzafon.
(d) And our suggestion that the Din of Shechting a Chatas in the north is confined to the Sa'ir Nasi is based on the word "Oso", which is a 'Miy'ut'.

8)
(a) Now that we include all Chata'os in the Din of Tzafon (from the third Pasuk), we try to learn from "Oso" 'Oso ba'Tzafon, ve'Ein Sa'ir Nachshon ba'Tzafon'. We might otherwise have thought that Sa'ir Nachshon required Tzafon - because it required Semichah.
(b) This D'rashah goes like Rebbi Yehudah, who learns from the Pasuk "Ve'samach Yado al Rosh ha'Sa'ir" - 'Lerabos Sa'ir Nachshon'.
(c) Rebbi Shimon learns from this Pasuk "Lerabos Se'irei Avodas-Kochavim li'Semichah'. The problem is now - according to Rebbi Shimon, why we will need to preclude Sa'ir Nachshon from Tzafon from "Oso".
(d) Mar Zutra b'rei de'Rav Mari counters this Kashya. He queries our initial contention, linking the Din of Tzafon to that of Semichah - due to the principle 'Mai de'Israbi Israbi ... ' (What the Torah includes [Semichah] it includes ... . But that is no reason to think that we will also include Tzafon).

9)
(a) We cannot still need "Oso" to preclude Se'ir Nachshon from Tzafon, to avoid learning it from a Binyan Av from other Chata'os - because if Se'ir Nachshon was considered a regular Chatas, then why would we need "ve'Samach Yado ... " to include it in the Din of Semichah?
(b) At the end of the day, we need a Pasuk to include Se'ir Nachshon in the Din of Semichah - because otherwise, we could not learn Sha'ah from Doros.
(c) And it is by the same token - that we do not need "Oso" to preclude Se'ir Nachshon from Tzafon.

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