What is the Minchas Bikurim? Why is it called by this name?
Rashi: The Minchas Bikurim, so-called because it is brought from the first of the ripening crops, is the Minchah that accompanies the Omer.
From what is Minchas ha'Omer comprised?
Rashi: It is from the first of the barley harvest to ripen. 1
Seeing as the Minchas ha'Omer is obligatory, why does the Torah write "Im"?
Rashi: This is one of three locations where the Torah writes "Im", even though it is obligatory. 1
Ramban #1, Moshav Zekenim #1: Since Hashem did not command to offer the Minchas ha'Omer now (in the Midbar), the Torah follows from the previous Pesukim. If you want to bring a Minchah Al ha'Machavas, do it like this ... a Minchas Marcheshes, do it like this ... and if you bring a Minchas Bikurim, bring it like this.
Ramban #2, Moshav Zekenim #2: "Im" is indeed conditional, seeing as Eretz Yisrael is given to Yisrael on condition that they behave. 2 What the Torah is therefore saying is that if Hashem brings Yisrael to Eretz Yisrael and they bring the Minchas Bikurim, this is how they should bring it. 3
Moshav Zekenim, citing R. Shimon in Toras Kohanim: If you offer it properly, I credit you as if you offered voluntarily. If not, I consider it an obligation. 4
Moshav Zekenim, citing R. Yehudah in Toras Kohanim: In the future, it will cease, and later return. It says "v'Im Yihyeh ha'Yovel" (Bamidbar 36:4) for the same reason.
The fact that the Torah inserts "Im" by virtually every Korban that it discusses throughout the Parshah seems to support the Ramban's two explanations. (EC)
Moshav Zekenim: We say that one who is commanded and fulfills is greater than one who is not commanded! Rather, if you offer it improperly, I consider it an obligation, that you offered it for yourselves, to permit Chadash, and not for Me.
What does Kaluy ba'Eish mean? Why was it done?
Rashi: It means that the barley was roasted on a fire in a pipe for roasting kernels, to dry them before they are ground.
What is the meaning of "Geres Carmel"?
Rashi #1: "Geres 1 Carmel" means 'ground (broken) up whilst it is still fresh (and moist).
Rashi #2: It implies that the barley is to be ground in a grits-grinders mill ('Rechayim shel G'rusos') which grinds grain coarsely - into two or four.
Rashi #3 (Sotah, 14a): "Geres" means choice quality barley, that has been sifted in thirteen sieves. 2
What is the exact meaning of "Carmel"?
Rashi: It is the acronym of "Car Malei" - meaning that the barley is still moist and full inside its husk.
Why do Kohanim eat [the Shirayim after taking Kemitzah from] the Omer? It is not for sin, rather, to permit Chadash. "V'Achlu Osam Asher Kupar Bahem" (Shemos 29:37) does not apply!
Moshav Zekenim: "L'Chol Minchasam" (Bamidbar 18:9) includes the Omer. It includes also Minchas Sotah, which is to clarify sin, and not to atone.