What are the implications of the phrase "Vezavachta Shelamim"?
Yerushalmi Chagigah, 1:4: It that they were to bring Zivchei Shelamim, a term that applies exclusively to animals - to preclude birds and Menachos. 1
See Torah Temimah in Re'ei, 16:14, citing Chagigah 5a, and note 60.
What is the reason for the Simchah?
Seforno: Because Yisrael entered into a covenant with Hashem at Har Gerizim and Har Eival.
Pesachim (109a): Because they ate the meat of Shelamim. 1
Pesachim, Ibid.: And we learn from here that, when the Beis-Hamikdash is standing, Simchah only applies when there is meat - some say Basar Kodshim, others, any meat. See Torah Temimah, citing Pesachim, Ibid., and note 4.
Seeing as Har Eival, on which the Mizbe'ach was built, was the mountain on which the K'lalos were said, why should they be happy?
Oznayim la'Torah: This teaches us to be happy with Yisurim (suffering), because when Hashem sends Yisurim, it is only for our good, Moreover, this was a prelude to conquering Eretz Yisrael, and Eretz Yisrael can only be acquired with Yisurim.
What are the implications of the word "Shelamim"?
Moshav Zekenim (16:15, citing Mo'ed Katan 15b): It implies when when one is Shalem (complete - his mind is settled), forbidding an Onein and an Aveil to eat Shelamim. 1
Shelamim is mentioned in almost fifty locations in the Torah. Although the Gemara did not say from which Pasuk the Chachamim learns it, presumably, they learn it from the current Pasuk, since it specifically mentions Simchah (PF).
