What are the connotations of "Korban Hashem"?
Rashi (in Zevachim, 113b): It means a gift to Bedek ha'Bayis (for the needs of the Mishkan) - which is also called a Korban 1 (and which we learn from here - Yoma, 43b).
Targum Yonasan: It means a gift in the Name of Hashem
See Torah Temimah, note 38.
What is the definition of "Etz'adah, of "Tzamid", of "Taba'as, of "Agil" and of "Kumaz"?
Rashi and Yerushalmi Shabbos, 6:4: They translate as feet-bracelets, bracelets, rings (worn on the fingers, ear-rings and an ornament worn on the womb (or on the breasts - Yerushalmi), 1 respectively.
Targum Yonasan: They brought 'the crowns from their heads, the necklaces from their necks, the ear-rings from their ears, the bracelets from their arms, the rings from their fingers and the 'Kumaz' from their chests'.
Rashi (in Vayakhel Sh'mos, 35:22) and Hadar Zekenim: "Kumaz" is the acronym for 'Ka'an M'kom Zimah' ('This is the place of Z'nus'). Rashi in B'rachos, 24a adds that they would pierce the walls of the womb - like one pierces ears for ear-rings - and fix the Kumaz to prevent them from being raped.
Why does the Torah list 'Kumaz' - that a woman wears inside her clothes) together with the ornaments that are worn outside?
Shabbos, 64b: To teach us that 'If one looks even at a woman's little finger (for pleasure), it is considered as if he looked at her private parts! 1
See Torah Temimah, note 42.
What are the connotations of "Lechaper al Nafshoseinu"? Why did the soldiers need a Kaparah?
Rashi and Ramban #1: To atone for the immoral thoughts 1 that they had when they looked at the Midyanite women.
Ramban #2: As a mark of gratitude to Hashem for having redeemed them from the sword and returning them safely from the battle-field.
Rashbam: Since being counted is subject to a plague, before they were counted, they made a Neder to donate a Korban ('for the Avodah of the Ohel Mo'ed') as a Kaparah to counter the threat. 2
Seforno: To atone for the sin of Pe'or, for failing to protest when the people sinned and they required a Kaparah to save them from destruction.
Targum Yonasan: When the soldiers entered the Midyanites' houses and saw their beautiful daughters, they removed all their golden ornaments and took them as spoil, but they avoided looking at them in order not to die the death of Resha'im in the world to come and in order that it should not stand against them on the great day of judgment. And they were now bringing their Kaparah as testimony of their innocence. 3
Shabbos, 64b: Because the men of that generation 4 feasted their eyes on the Ervah of the women.
Oznayim la'Torah: Based on the Gemara in Shabbos, 32a - that miracles detract from one's merits - they were afraid that, having experienced miracles in the total defeat of the enemy without ;losong a man, their sins now exceeded their merits.
Refer to 31:50:151:1-3.
Rashbam: Which they were duly bringing.
See Na'ar Yonasan.
It is not clear whether this refers to the soldiers - See answer #1 - or the people in general ... presumably with regard to when they sinned with the daughters of Mo'av by Ba'al-Pe'or.
Rashi (in Sh'mos 35:22) writes that Moshe rejected the women's donation of the copper mirrors for the Mishkan, until Hashem told him to accept them. Why did he accept the Kumaz as a Korban?
Riva #1: Because Kumaz is not on the womb itself.
Riva #2: Because the Kiyor was made from the mirrors alone, but the Kumaz was mixed together with other Keilim (and was therefore Bateil be'Rov).
Riva #3: The Kumaz was melted down, and was no longer intact, so Moshe did not object. The mirrors, on the other hand, were fixed intact into the Kiyor. 1
Riva: Which we know because the Torah writes there "va'Ya'as es ha'Kiyor... be'Mar'os ha'Tzov'os", and not mi'Mar'os ha'Tzov'os.
QUESTIONS ON RASHI
Rashi writes that the Korban atoned for immoral thoughts about B'nos Midyan. But even intimacy is permitted with an Eishes Y'fas To'ar?
Da'as Zekenim: One may take only one woman [per war], and be intimate with heronly once [before she converts]. One may not think about a second woman, or even about the first, after he has been intimate with her.
Sifsei Chachamim #1: The Heter of Y'fas To'ar only applied after the seven years of conquest and seven years of division, as implied by the Yerushalmi.
Sifsei Chachamim #2: The Heter of Y'fas To'ar only applies in an optional war, whereas this was considered an obligatory one - "Lo Sechayeh Kol Neshamah." Yisrael knew this only after Moshe became angry with them for not killing the women. If so, their thoughts about the women were forbidden.
Oznayim la'Torah #1: Eishes Y'fas To'ar is only permitted Bedi'eved to counter the Yeitzer ha'Ra, whereas the troops who fought against Midyan overcame the Yeitzer ha'Ra by themselves.
Oznayim la'Torah #2: The battle against Midyan came about because they rendered the women Hefker to commit Z'nus. It would therefore have made no sense for the avengers to give vent to their Yeitzer ha'Ra by taking those very same women during the battle of vengeance.
Intimacy with an Eishes Y'fas To'ar may be permitted, but (independent) immoral thoughts are not.
