Why must she remove the clothes in which she was captured?
Rashi and Ramban #2 (on Pasuk 12): She must change from the beautiful clothes that she wore during the battle to distract the enemy and lure them into committing adultery with her instead of fighting.
Ramban #1 (on Pasuk 12) and Rashbam: She must change into mourning attire. 1
Why does the Torah see fit to add "Veyashvah Veisecha"?
Rashi: When her captor enters the house he stumbles over her and when he leaves he stumbles over her and sees her in her state of ugliness. 1
Ramban (on Pasuk 12): She may not leave his house during the month-long period of mourning. 2
What is the significance of crying for her father and mother?
And mourning over her father and mother from whom she has been separated.
All in order to discourage him from retaining her. The Ramban too, cites this as the reason for the obligation to induce her mourning - Refer to 21:13:3:2.
Ramban: Presumably, Beis-Din Tovel her against her will - like they Tovel Avadim, and it is because she is being converted against her will that the Torah forbids her on her captor during this entire period.
Why the month-long mourning period?
Ramban #1: Refer to 21:13:3:1.
Ramban #2 (citing the Ibn Ezra): The Torah allows her to mourn and weep for the loss of her parents like one weeps and mourns the loss of a relative - in honor of her parents.
Ramban #2 (citing the Moreh Nevuchim): It is out of pity for the captive, since crying and mourning helps remove the pain and calm him down. 1
Ramban #3: It is to remove from her mouth and from her heart all mention of Avodah-Zarah and to snuff out all lingering thoughts about her parents and her people. 2
What are the implications of the word "Uve'altah"?
Ramban #1 (citing the Sifri): The only thing he has to do with her is to be intimate 1 with her, because Kesef and Sh'tar do not take effect on her.
Ramban #2: It is only after the period of mourning has ended that he is permitted to be intimate with her. 2
Ramban: In fact, even the Bi'ah is not as an act of betrothal, seeing as she is still a Nochris - when he performs the first Bi'ah. See also Ramban, DH 've'Al Derechy ha'P'shat'.
Ramban: And when the Torah wrote earlier "Vechashakra bah Velakachtah l'cha le'Ishah" it meant that he may take her with the intention of living with after he has fulfilled everything that is written in the Parshah. See R. Chavel's notes, that this is also the opinion of Rashi in Kidushin, 21b). See Ramban, DH 'Aval Ra'isi' citing the Yerushaslmi, Makos, 2:6.
When and how does she become his wife?
Ramban (citing Kidushin, 22a and the Sifri): At the end of the period of mourning she automatically becomes his wife - because the Torah acquires her to him.