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1)
(a) Had the Torah written "Lo Yasim Alehah ... ve'Lo Yiten" (without adding the second "Alehah"), we might have thought - that it requires two Kohanim in order to be Chayav two La'avin (i.e. one Kohen would only receive one Malkos, even if he transgressed both La'avin).
(b) "Alehah" comes to teach us - that the two La'avin are connected with the Minchah, irrespective of whether it is one Kohen or two Kohanim who transgress them.
(c) The Tana also learns from the second "Alehah" - that one is only Chayav if one places the actual oil or Levonah on the Minchah, but not the K'li that contains it.

2)
(a) Our Mishnah discusses all the possible computations regarding which Menachos require Hagashah but not Tenufah, which require Tenufah but not Hagashah, which require both and which require neither. The Tana places a Minchas So'les, Machavas, Marcheshes, Chalos, Rekikin, Minchas Kohanim, Kohen Mashi'ach, Nochrim, and Nashim - in the group that requires Hagashah, but not Tenufah.
(b) We already discussed Rav Papa, who states (according to one interpretation) that the Mishnah always refers to ten cases. The above list only contains nine. Instead of Minchas ha'Omer (which appeared in the previous Mishnah, but does not belong here), the Tana inserts - Minchas Chotei.
(c) Rebbi Shimon (who will later insert two cases) omits from the list - the Minchas kohanim and the Minchas Kohen ha'Mashi'ach.

3)
(a) The Pasuk writes (in connection with the Minchas Marcheshes) "Ve'heivesa es ha'Minchah Asher Ye'aseh me'Eileh la'Hashem ... Ve'higishah el ha'Mizbe'ach". We learn from the word ...
1. ... "ha'*Minchah*" - that not only the Kemitzah requires Hagashah, but so does the entire Minchah (before the Kemitzah is performed).
2. ... "*ha*'Minchah" - that the Mitzvah of Hagashah extends to a Minchas Chotei.
(b) We cannot learn Hagashah by Minchas Chotei with a 'Binyan Av' from ...
1. ... Minchas Nedavah - because the latter requires Shemen and Levonah, whereas it does not.
2. ... Minchas Sotah - because the latter requires Tenufah, which it does not.
(c) So we try to learn it with a 'Tzad ha'Shaveh' from a Minchas Nedavah and a Minchas Sotah, which share with it - the obligation to perform Kemitzah, creating the basis for a Tzad ha'Shaveh'.
(d) We ask on the 'Tzad ha'Shaveh' - that whereas they both apply to an Ashir as well as to an Ani, a Minchas Chotei is confined to an Ani (hence we need to learn it from "*ha*'Minchah").

4)
(a) Rebbi Shimon includes in the Din of Hagashah, a Minchas ha'Omer from "Ve'heivesa and a Minchas Sotah from "Ve'hikrivah" (both mentioned in the Pasuk that we are currently discussing) - on the basis of Pesukim in connection which use similar words ("Va'haveisem es Omer ... " [Emor] and "Ve'hikriv Osah el ha'Mizbe'ach" [Naso]), regarding these Menachos respectively.
(b) We try and learn Minchas Sotah from Minchas Chotei - because if the latter, which does not require Tenufah, requires Hagashah, the former, which does require Tenufah, certainly should.
(c) We ask on ...
1. ... the Limud from Minchas Chotei is - that it consists of wheat (like most other Menachos do, whereas the Minchas ha'Omer consists of barley).
2. ... the Limud from Minchas ha'Omer (which we initially bring in its place) - that it requires Shemen and Levonah (which the Minchas Chotei does not).
3. ... the 'Tzad ha'Shaveh' (from both of them), which forces Rebbi Shimon to learn it from "Ve'hikrivah" - that they may not be brought in the form of Kemach (unsifted flour), only as So'les (whereas the Minchas Sotah may).

5)
(a) Rebbi Yehudah in the Beraisa, learns Hagashah by Minchas Sotah from "Ve'heivesa" - on the basis of a Pasuk in Naso, which uses a similar expression in connection with Sotah ("Ve'heivi es Korbanah Alehah").
(b) And as far as the Minchas ha'Omer is concerned, he says - that does not require a Pasuk to include it in the Din of Hagashah, as we shall now see.
(c) From "Ve'hikrivah" - Rebbi Yehudah precludes the Minchas Nesachim, the Sh'tei ha'Lechem and the Lechem ha'Panim from Hagashah.

6)
(a) We refute ...
1. ... the 'Kal va'Chomer from Minchas Chotei (based on Tenufah) - with the Pircha 'Mah le'Minchas Chotei she'Kein Ba'ah Chitin ... '.
2. ... the counter proof from Minchas Sotah which consists of barley (just like the Minchas ha'Omer) - with the Pircha 'Mah le'Minchas Sotah she'Kein Ba'ah Levarer Avon' ...
(b) ... which we answer with 'Minchas Chotei Tochi'ach'.
(c) Rebbi Yehudah finally learns Hagashah with regard to Minchas ha'Omer - from a 'Mah ha'Tzad' between Minchas Chotei and Minchas Sotah.

7)
(a) Rebbi Shimon (who learns Minchas ha'Omer from "Ve'heivesa") disagrees with this - because he claims, they are more common than the Minchas ha'Omer, which is brought only once a year.
(b) Rebbi Yehudah counters Rebbi Shimon's Pircha - in that to the contrary, the Minchas ha'Omer is definitely brought once a year, whereas Minchas Chotei and Minchas Sotah might never be necessary (a bird in the hand ... ).
(c) Querying Rebbi Yehudah, we ask that perhaps "Ve'heivesa" comes to teach us a Minchas Nedavah not mentioned in the Parshah - by which we mean a Minchas Nedavah consisting of barley.
(d) This suggestion is based on the fact - that a Minchas Chovah comprises Menachos of wheat and of barley (the Minchas ha'Omer), maybe a Minchas Nedavah does too.

8)
(a) We refute the current suggestion however - from the word "Eileh" (in the same Pasuk in Vayikra), confining the Minchos Nedavah to those listed in the Parshah.
(b) And from the 'Mem' of "me'Eileh", we learn - that a Yachid may bring any one of the five Menachos listed in the Parshah (and that he is not obligated to bring them all).

9)
(a) Rebbi Shimon learns from "es ha'Minchah" - that 'other Menachos' (shel Nochrim, Nashim ve'Chotei) are included in the Din of Hagashah.
(b) And from "me'Eileh" he precludes - the Sh'tei ha'Lechem and the Lechem ha'Panim.
(c) He include Sha'ar Menachos and exclude the Sh'tei ha'Lechem and the Lechem ha'Panim, and not the other way round - because the latter are completely eaten, and no part of them is brought on the Mizbe'ach.
(d) The problem this creates regarding a Minchas Nesachim is - why we do not then include it in the Din of Hagashah, seeing as all of it goes on the Mizbe'ach?

10)
(a) We solve the problem by precluding the Minchas Nesachim from Hagashah from "Ve'hikrivah". Rebbi Shimon did indeed already use "Vehikrivah" to include a Minchas Sotah in the Din of Hagashah. However - that was from the word "Ve'hikriv', whereas the current D'rashah is from the 'Hey' at the end of the word.
(b) Rebbi Shimon includes the Minchah of a Nochri, a Chotei and a woman, and excludes a Minchas Nesachim - because the latter is not an independent Korban, like the former are (see also Tosfos 61a DH 'u'Ba'os').
(c) The problem this create with Minchas Kohanim and Minchas Kohen ha'Mashi'ach is - that they are independent Korbanos, yet they do not require Hagashah?
(d) We answer that "Ve'higishah el ha'Mizbe'ach" comes to preclude them from Hagashah. But surely we need that to teach us the Din of Hagashah.

11)
(a) We conclude that Rebbi Shimon includes Minchas Nochrim, Chotei ve'Nashim (from "ha'Minchah") because they have four advantages that the three Menachos precluded by him do not have. Two of the advantages are 'le'Ishim' and 'Ba'os bi'Gelal Atzman', the third is - 'Yesh Meihen le'Kohanim'.
(b) We do not therefore include ...
1. ... the Sh'tei ha'Lechem and the Lechem ha'Panim - because no part of them go on the Mizbe'ach.
2. ... the Minchas Nesachim - because it is not an independent Korban.
3. ... the Minchas Kohanim and the Minchas Kohen Mashi'ach - because none of it is given to the Kohanim.

12)
(a) The Pasuk in Vayikra continues "Ve'heirim ... es Azkarasah" - which means either with a K'li or with the kohen's hands.
(b) The Beraisa learns from the Pasuk in Tzav "Ve'heirim Mimenu - be'Kumtzo" that here too, he must separate the Kometz with his hands.

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