R. Bachye #1 (on Pasuk #5, citing the Ibn Ezra): Because it was customary to dance (to the tune of flutes - Chalilim) in the vineyards.

R. Bachye #2: It is a Lashon Chulin - The fourth-year fruit on the tree remains Kadosh until the owner redeems it and renders it Chulin.

Sotah, 44a: To incorporate in the current Halachah someone who betrothed a woman, irrespective as to whether she is a virgin, a widow or if she is a Shomeres Yavam - and even if there were five brothers and one of them died, they are all sent home. ¹

Yerushalmi Sotah, 5:6: It implies that he is sent home, even if he is a Bachur who betrothed a widow or a widower who betrothed a virgin. ¹

Sotah, 44a: It comes to preclude a Kohen Gadol who betrothed a widow, a Kohen Hedyot who betrothed a Gerushah or a Chalutzah and a Yisrael who betothed a Mamzers and a Nesinah, who are not sent home from the battle-front. ¹

R. Bachye: It implies that whoever dies in battle dies prematurely - before his allotted time in this world has expired. ¹

Kidushin, 13b: To teach us that the death of her husband permits a woman to remarry. ¹

Refer to 20:5:5:1.

Sotah, 44a: It teaches us Derech Eretz - that a man should first build a house and plant a vineyard before getting married. ^{1 2}

Maharsha (in Sotah, 44a): He may do whichever one suits him best. ¹

Rashi: Because if they disobey the Kohen's ¹ orders to return home, they deserve to die.

Ramban #1 (in Pasuk 8, according to R. Yossi ha'Gelili): One who sinned is afraid. He thinks that his sins may cause him to fall in battle. The Torah is covering up for him - inasmuch as people will now assume that he is returning due to a vineyard, house or wife.

Ramban #2 (in Pasuk 8, according to R. Akiva): If, after the Kohen's assurance, he is still afraid - he lacks Bitachon and will not merit the miracle of salvation that the Kohen promises.

Targum Yonasan: Because they left the relevant Mitzvah unfulfilled - the first one one did not fix a Mezuzah to his door, the second one did not redeem the fruit of his vineyard and the third one did not marry his betrothed. ²

Kidushin 13b: We can learn from here that a husband?s death permits a woman to get married. ¹

Rashi (in Devarim 24:5): The Chasan during his first year of marriage ¹ may not leave his house for anything connected with war, neither to provide the army with water and food, nor to prepare the roads (sappers), whereas all those whom the Kohen sends back from the front ... are still required to provide water and food and to prepare the roads.