Why does the Torah mention 'Simchah' once on Shavu'os, twice on Sukos and not at all on Pesach?
Ba'al ha'Turim: It mentions it once on Shavu'os - because the grain has been harvested, twice on Sukos - because everything has been gathered into the house, and not at all on Pesach - since no harvest has yet taken place.
Bechor Shor and Da'as Zekenim and Rosh (both on Pasuk15): Pesach is not a time of Simchah of gathering grain; it is to remember the miracle of Yetzi'as Mitzrayim. Shavu'os is a time of Simchah of the grain harvest, and all the more so Sukos, 1 when everything has been gathered in from the field. 2
Oznayim la'Torah: Because on Pesach when the Torah has not yet been given, there is no Simchah because whatever bounty we receive is likely to be used in pursui of our own physical pleasure and not for the sake of Hashem. On Shavu'os, our undertaking to accept the Torah brings with it a measure of Simchah - so the Torah mentions Simchah once; Whereas on Sukos, following the Yamim Noro'im , when we have done Teshuvah and on Sukos itself, when we are busy with actually carrying out the Mitzvos that we accepted on Shavu'os, the Simchah reahes its zenith and the Torah writes it three times.
Da'as Zekenim and Rosh: The Torah writes a third Simchah in connection with Sukos
What are the connotations of "Vesamachta be'Chagecha"?
Yerushalmi Chagigah, 1:2: It teaches us via a Gezeirah Shavah "Vesamachta" "Vesamachta" from Ki Savo, 27:7 in connection with Har Gerizim and Har Eival, that the obligation of Simchah must be performed by eating Shalmei Simchah on Yom-Tov. 1
Why does the Torah specify four kinds of poor people?
Rashi: 'If you will make Mine happy,' says Hashem, 'I will make yours happy
By inviting them to your table to share your Shalmei Simchah and Shalmei Chagigah.
The Seforno does not mention the Levi, who presumably, will rejoice with the Ma'aser that he receives.
Simchah usually only applies to meat (Pesachim 109a), so why didn't he explain like Rashi, that others have a Mitzvah to give to them? Perhaps he teaches that others need not give to them grain, which they can take themselves. (PF). Hashem is indeed referring to what He (not the Yisrael) will give them - and they can subsequently trade the Leket and Pe'ah for meat.
Why does the Torah refer here to the location that Hashem will choose?
Ramban #1: To teach us that, once the Beis-Hamikdash has been built, we will not assemble to bring the Korbanos of Yom-Tov anywhere else. 1
Ramban #2: To exempt from Aliyah le'Regel three times a year until Hashem chooses a place to rest His Shechinah .
Ramban: And it repeats this in Pasuk 16. See also Pasuk 5. (The Sifri and the other Midrashim include also Shilo. Perhaps the Ramban mentioned only the Beis Hamikdash because once it has been built, there will not be another place. - PF)
