What is the significance of the Chorim? Why does the Torah mention them here?
Rashi: To demonstrate that, just as Hashem helped Mo'av to inherit their land by driving out the Eimim, so too, did He help the B'nei Eisav to inherit their land by driving out the Chori, who lived there before them. 1
Seforno: The Torah inserts what happened to the Eimim and the Chori here to teach us that although Mo'av and Eisav drove them out in order to protect their land, increasing it in size and leaving much of it uninhabited, Yisrael did not exploit the situation and pass through those sections of land, but went round both countries as instructed.
Rashi: And the Torah will repeat the message with regard to Amon driving out the Refa'im (whom they called 'Zamzumim') to inherit their land. Also this was not Eretz Refa'im that Hashem gave to Avraham.
Ramban: As is evident from the Pasuk in Bereishis 36:2, 36:20). See Ramban, DH 've'Zehu', who elaborates on the names 'Chivi' and 'Chori'. Refer also to 2:23:1:4*, where the Ramban also equates the Chivi with the Refa'im.
Ramban: And to take it away from them would constitute theft, just as to take away the land of Cana'an after Yisrael inherited it would constitute theft as the Pasuk specifically states.
Why did Hashem give Har Se'ir to Eisav?
Rashi (in Divrei ha'Yamim 1, 1:1): a. Due to his love of Yitzchak and b. to keep the promise that He had made to him to increase his children and to rule over all.
Targum Yonasan: Refer to 2:5:2:1*.
What is the Pasuk referring to when it writes "Ka'asher Asah Yisrael le'Eretz Yerushaso"?
Ramban: It refers to the land of the seven nations of Cana'an. 1
Seforno: It refers to the land of Sichon and Og, which Yisrael had already miraculously captured.
Even though they had not yet conquered it. The Ramban concludes that the Torah has now explained how all the descendents of Avraham inherited their respective lands in miraculous ways - Mo'av, Eisav, Amon and Yisrael.
Why does the Torah write "Yirashum" in the future?