Why does the Kohen insert "Ki Hashem Elokeichem ... " here?
Rashi: To remind them that, whereas the enemy are going to war relying on the strength of flesh and blood, 1 you go to war relying on Hashem's strength (good enough reason not to be afraid - Torah Temimah).
Ramban: To warn them not to rely on their own might and prowess, but on that of Hakadosh-Baruch-Hu. 2
Rashi: Like we find in Shmuel 1, Perek 17, when the P'lishtim went to fight Yisrael relying on the might of Golyas - and see what happened to him in the end!
Ramban: As the Pasuk writes in Tehilim, 146:3, 147:11 "Al Tivt'chu bi'Nedivim ... Rotzeh Hashem es Yere'av, es ha'Meyachalim le'Chasdo."
Why does the Kohen insert the (otherwise superfluous) words "Haholech Imachem"?
Rashi: He is referring to the Machaneh ha'Aron. 1
See Sifsei Chachamim and refer to 20:4:151:1-5.
What are the connotations of "Lehilachem lachem" and of' "Lehoshi'a eschem"?
Ramban: It means 'to destroy your enemies and to save you from their hands, so that not one of you will fall in battle'. 1
Ramban: Which explains why Yehoshua cried out to Hashem when, in the battle against Ay, thirty-six men of Yisrael fell - See Yehoshua, 7:7-9.
What is the 'Machaneh ha'Aron' to which the Pasuk is referring?
Sotah, 42a: It refers to the Aron 1 which contained the broken Luchos.
Maharsha (in Sotah, 42a): It refers to the Shechinah.
Yerushalmi Sotah: Some say that it is Hashem's name, which was placed inside the Aron.
Yefei Mar'eh (on Yerushalmi Sotah 8:3): It is the Machaneh Leviyah.
With reference to Machaneh Yisrael, who took the Aron with them to war (Torah Temimah).