What is the definition of "Mikreh Laylah"? Why does the Torah insert the word "Laylah"?
Rashi: "Mikreh Laylah" is an emission that occurred at night-time not to preclude a day emission, but), because this is something that normally occurs at nighttime.
Which camp is the Torah instructing a soldier who has an emission to leave?
Rashi and Ramban #2 (citing Pesachim, 88a): With reference to wartime - when the Aron accompanied Yisrael into war - the Torah is ordering the soldier with an emission, via an Asi and a Lo Sa'aseh, to leave the Machaneh Shechinah and the Machaneh Leviyah. 1
Ramban #1, Targum Onkelos and Targum Yonasan: It is instructing a soldier who has an emission to leave the camp of Yisrael during wartime. 2
See Sifsei Chachamim. Ramban: And the Torah requires also covering one's excrement, based on the Gemara in B'rachos, 22b which requires excrement to be covered when mentioning the Name of Hashem during the Amidah and the recital of the Sh'ma. Refer to 23:10:1:3.
Ramban: The reason that which the Torah gives in Pasuk15 - "Because Hashem goes in the midst of the camp to save you ... " pertains to all the Mitzvos in Pesukim 11, 12, 13 & 14, to keep the camp holy and clean - as this causes the soldiers to focus their hearts towards Hakadosh-Baruch-Hu (as opposed to relying on their superior strength), and to hope for His salvation (because the Camp of Yisrael is like the Mikdash Hashem. Consequently, it is from here that Chazal learn that, when Davening, one should keep away four Amos from excrement).
Why is a person who has an emission obligated to leave the camp?
Ramban: Refer to 23:11:2:2.