Why does the Torah need to mention Zachar and Nekeivah?
Eruvin, 104b: To preclude K'lei Cheres, which, unlike Zachar and Nekeivash, are subject to Av ha'Tum'ah, 1 and which are therefore not subject to the La'av.
Nidah, 28b: 'Zachar Vadai, Nekeivah Vada'is' - to preclude a Tumtum and an Androginus who saw Zivus or Nidus 2 from the La'av of Bi'as Mikdash. 3
Sifri: The Torah writes "mi'Zachar ad Nekeivah" and not 'me'Ish ad Ishah' on order to incorporate Ketanim in the Din of Shilu'ach Machanos. 4
Having written in Pasuk 2 "Viyeshalchu min ha'Machaneh", why does the Torah add the phrase "el mi'Chutz la'Machaneh Teshal'chum?
Pesachim, 95b: "Min ha'Machaneh" implies from part of the Machaneh (the Heichal), whereas "mi'Chutz la'Machaneh" implies from the entire Machaneh (even from the Azarah). Consequently, the Torah is teaching us that one only transgresses "Viyeshalchu min ha'Machaneh" (from the Heichal) where the obligation to leave the Azarah applies, and that if by a Pesach ha'Ba be'Tumah, 1 where Teme'im are permitted to enter the Azarah, a Tamei Meis who enters the Heichal is not subject to "Viyeshalchu min ha'Machaneh".
Sifri #1: Because we would otherwise have thought that the main objective is to keep him away from the Aron and from those who are carrying it 2 and that it will therefore suffice to alot for him a location inside the camp at a distance from the Aron.
Sifra #2: To include a Tumtum and an androginus who became Tamei via a form of Tum'ah which was not Nidus or Zivus. 3
Sifri #3: To include Keilim and Teme'im who cannot be sent outside the camp. 4
Why does the Torah add the phrase ve'Lo Yetam'u es Machaneihem"?
Pesachim, 67a: The Torah writes "es Machaneihem" (plural) to teach us that Teme'ei Meis and Zavim who are sent out of the camp are sent to different locations. 1
A Tamei Meis must is sent only out of the Machaneh Shechinah, a Zav out of Machaneh Leviyah as well (and a Metzora, even out of Macheneh Yisrael) See Torah Temimah, note 13.
See Torah Temimah, note 14.
Makos, 15a: And, in spite of the fact that a 'La'av ha'Nitak la'Asei' is Patur from Malkos, the perpetrator is Chayav Malkos, since it is 'La'av she'Kadmo Asei', where the Asei is applicable already before the La'av - See Torah Temimah, note 15.