What is the difference between "Mele'ascha" and "Dim'acha"?
Rashi and Ramban #1 (citing Targum Onkelos and the Mechilta): "Mele'ascha" refers to Bikurim 1 and "Dim'acha to Terumah. 2
Ramban #2: "Mele'ascha refers to corn and to wine and oil, 3 with which one fills up the storehouses - or "Mele'ah" is a Lashon of B'rachah, with reference to storehouses of corn, wine and oil, whereas "Dim'acha" refers to wine and oil. 4
Rashbam and Seforno: "Mele'ascha" refers to the Terumah of one's grain, like it says "ha'Melei'ah ha'Zera"' (Devarim 22:9), and "Dim'acha to the Terumah of one's wine and oil, which are clear like Dema'os (tears - Rashbam).
Targum Onkelos and Targum Yonasan: The Bikurim of one's grain and of one's wine and oil, respectively.
Hadar Zekenim #1: "Mele'ascha" refers to males, because, when a boy is born, there is 'Simchah Mele'ah'. And "Dim'acha" to females, who shed [many] tears. 5
Hadar Zekenim #2 (citing R. Yosef Karo): "Mele'ascha" is a wife, about whom the Pasuk writes in Koheles 11:5 "be'Veten ha'Mele'ah", and "Dim'acha", children, since they are a mixture of the seed of the man and woman.
Taken from grain which the Torah calls 'Mele'ah' in Devarim 22:9 (Ramban and Rashbam). Rashi, Riva and Rosh: It is an obligation that comes when your grain is full and ripens - Bikurim.
Ramban: So-called because it is brought from wine and oil, rather then from grapes and olives. Rosh - it is something that drips and is clear, like tears - Terumah of wine and oil. See Torah Temimah, note 218, citing Rashi, who elaborates.
Ramban: As in Devarim 22:9 and Bamidbar, 18:27, respectively.
Ramban: 'Dim'ah' defines anything that drips, not only tears. The Ramban (in this explanation) does not clarify whether this applies to Bikurim or to Terumah.
Tosfos ha'Shalem 8, footnote 1): 'If you give the B'chor to Me, the rest will be blessed (What is the Isur in delaying females? Perhaps he means that in the merit of giving the B'chor to Me, you will not delay to be blessed with sons and daughters - PF).
What are the connotations of "Lo Te'acher"?
Rashi (citing the Mechilta) and Ramban #2 (citing the Mishnah in T'rumos, 3:7): It is a prohibition against changing the order of Matanos - a. Bikurim, 1 b. Terumah, and c. Ma'asros (Ma'aser Rishon, and d. Ma'aser Sheni - Ramban). 2
Rashbam: It teaches us that one should not fail to give Terumah before Ma'asros.
Targum Yonasan: It is a prohibition against delaying to bring one's Bikurim to the Beis-ha'Mikdash.
Hadar Zekenim #1: It is a Mitzvah to give one's B'chor to Hashem (to redeem him). 3
Hadar Zekenim #2 (citing R. Yosef Karo): It is a prohibition against delaying getting married. One should marry at eighteen and have children, and then 'Give your B'chor to Me.'
What does "B'chor Banecha Titen Li" entail?
Rashi: It entails redeeming one's firstborn son from a Kohen for five Sela'im. 1
Seforno: It entails giving one's B'chor to Hashem to serve in the Beis-ha'Mikdash and to teach Torah. 2
Targum Onkelos and Targum Yonasan: It entails designating them for Hashem. 3
As the Torah writes in Korach, Bamidbar 18:16.
In the same way as the Torah will later command the Kohanim, after the episode of the Golden Calf, as the Navi indicates in Mal'achi, 2:7 (Seforno).
Presumably, they mean to explain like answer #2. See also Yayin ha'Tov.
Having already taught the Din of B'chor Adam in Sh'mos 13:13, why does the Torah need to repeat it here?
Rashi: In order to juxtapose the Din of B'chor Beheimah to that of B'chor Adam - inasmuch as, just as one redeems a firstborn baby after thirty days, so too, should one hold on to a B'chor Beheimah for seven days before giving it to a Kohen. 1
Seforno: To teach us that, just as one gives a B'chor Adam to Hashem when it has left the realm of Safek Nefel (after thirty days), so too, must one give a B'chor Beheimah to Hashem when it has left the realm of Safek Nefel (after eight days).
Rashbam: Refer to 22:29:0.1:1.
QUESTIONS ON RASHI
Rashi writes that "Dim'acha" refers to Terumah. What is the source?
Rashi (in Temurah, 4a): Because it is Medama'as - it mixes and becomes Bateil in a hundred and one of Chulin. 1
Moshav Zekenim: 'Dema' refers to a liquid, 2 and the Torah presents Terumah in its liquid form, 3 when it writes in Korach, 18:12 "Kol Cheilev Yitzhar ve'Chol Cheilev Tirosh". 4
Se Torah Temmah, note 218, who elborates.
As the Pasuk writes in Tehilim, 80:6 "Va'tashkemo bi'Dema'os Shelish".
As opposed to Bikurim, which one brings specifically in the form of fruit, and not liquid.
Moshav Zekenim: And not 'Cheilev Zayis ve'Cheilev Anavim'.Riva (citing R"M of Pontaiza). In fact, two of the three species that are subject to Terumah may be brought in liquid form (as wine and oil), as the MIshnah states in Terumos 11:3; only grain may not. On the other hand, most Bikurim may not be brought as liquids, since, based on the word "Tavi" - in 23:23, the Chachamim require Bikurim to be brought in solid for, with the exception of grapes and olives.