Why does the Torah need to add "Kein Tarimu Gam Atem"?
Rashi: To teach the Levi'im that they are required to separate Terumah from their Ma'aser (Rishon) in the same way as Yisrael separate Terumah from their crops - because Ma'aser is their inheritance.
Bava Metzi'a, 22a: "Atem", 'Gam Atem': To teach us a. that, just as a person knows when he separates Terumah, so too can his Shali'ach only separate Terumah with the knowledge and consent of the owner; b. that a Shali'ach who takes Terumah, like the owner (the Levi), 1 must be a Jew - to disqualify a Nochri from acting as a Shali'ach on his behalf to Ma'aser his crops. 2
Sifri: "Kein Tarimu" - to include a Levi; "Gam Atem" - to include a Kohen in the obligation to separate Ma'ser Rishon and T'rumas Ma'aser from his crops. 3
Kidushin, 41b: "Atem", 've'Lo Shutafin ... ve'Lo Apotropsin ... ve'Lo ha'Torem es she'Eino she'Lo' - to preclude partners, managers of the estate of orphans 4 and Terumah that Reuven separated on behalf of Shimon without his consent from taking effect.
Since the Levi himself is a Sha'li'ach who serves in the Beis-Hamikdash on behalf of Yisrael - See Oznayim la'Torah.
See Torah Temimah, note 106 & 107.
See Torah Temimah, note 106, who elaborates at length.
See Torah Temimah, note 108, who citing the Rashba, exdplains that the first two cases are Asmachtos (mi'de'Rabbanan).
Why does the Torah write T'rumas Hashem" and not 'Terumah la'Hashem'?
Kidushin, 53a: Because 'Terumah la'Hashem would render Terumah Asur be'Hana'ah, and the Kidushin of a Kohen who betrothed a woman with it would be invalid. 1 Now thar it writes only T'rumas Hashem, Terumah is not Asur be'Hana'ah and the Kidushin is valid.
As is the case by Ma'aser Sheini. See Torah Temimah, note 109.
Why does the Torah write "mi'Kol Ma'asroseichem" (plural)?
Yerushalmi T'rumos, 1:1: To compare all Ma'asros to each other - to teach us that just as a Katan cannot separate Ma'aser Dagan, 1 so too, can he not bring Ma'aser Beheimah.
Yerushalmi T'rumos, 2:1: The words also imply that T'rumas Ma'aser can be taken from anywhere - even if part is in Yehudah and part in Galil, and does not need to be 'min ha'Mukaf' 2 - all placed next to the batch from which the owner is taking.
What are the implications of the words "u'Nesatem mimenu es T'rumas Hashem"?
Yerushalmi Chalah, 2:3: It implies that what one gives to the Kohen should be sufficiently Chashuv to fall under the category of 'Matanah'. Consequently, the Chachamim 1 fixed the Chalah of a Balabos, whose dough is small, at one twenty-fourth and that of a baker, at one forty-eighth.
See Torah Temimah, note 112.
Bearing in mind that Aharon never entered Eretz Yisrael, why does the Torah write "le'Aharon ha'Kohen"?
Sanhedrin, 90b #1: To teach us that, one day, Aharon will come back to life and we will give him Terumah - a hint at Techiyas ha'Meisim.
Sanhedrin, 90b #2: To teach us that one should give one's Matnos Kehunah to a Kohen Talmid-Chacham (like Aharon), and not to an Am ha'Aretz. 1
See Torah Temimah, note 114.
Why does the Torah add the (otherwise superfluous) word "le'Aharon ha'Kohen"?
Yerushalmi T'rumos, 2:1: To teach us that one may give Aharon whatever he is able to eat in his capacity as a Kohen - in which case one is permitted to separate Matnos Kehunah from Tahor crops on to Tamei ones. 1
Yerushalmi Chalah, 3:2: To teach us that one should give Aharon whatever he is able to eat in his capacity as a Kohen - in which case it is forbidden to be Metamei Tevel before giving it to the Kohen.
See Torah Temmiah, note 115.