What is the translation of "Ki Orish Goyim"?
Rashi, Targum Onkelos and Targum Yonasan: 'When I will drive out the nations'.
What is the significance of the phrase "Vehirchavti es Gevulechah"?
Rashi: Because many people will then live far from the Beis ha'Mikdash 1 and will not be able to visit there often, that Hashem instigated the Mitzvah of Aliyah le'Regel three times a year.
Rosh: This alludes to receiving the land of Sichon and Og, which was not promised to Avraham. 2
What is the significance of the fact that 'Hashem will drive out [the Cana'ani] nations?
Da'as Zekenim, Hadar Zekenim and Rosh: Due to this, they will not covet your lnd when you travel to Yerushalayim for the Yamim-Tovim. 1
Da'as Zekenim, Hadar Zekenim and Rosh: Because 'If their G-d dispossessed us of our of what we previously owned, we will certainly not be able to conquer their land when they fulfil His Mitzvos and go to Yerushalayim for the Yamim'Tovim!'
What are the implications of "ve'Lo Yachmod Ish es Artz'cha"?
Pesachim 8b #1: It implies that the Mitzvah of Aliyas ha'Regel (going to Yerushalayim on Yom-Tov) is is confined to someone who owns land [in Eretz Yisrael].
Pesachim 8b #2 (according to Isi ben Yehudah): It teaches us that someone who goes to Yerushalayim for Yom-Tov] will leave his cow grazing in the meadow and his chicken pecking in the wasteheap, and Chayos and weasels will not attack them. 1
Pesachim (Ibid.): Due to the principle 'Sheluchei Mitzvah Einan Nizokin' (which we learn from here). The Gemara concludes thowever, that we learn it from the Pasuk in Re'ei Devarim, 16:7 "u'Fanisa va'Boker Vehalachta le'Ohalecha", which teaches us that even upon their return from Yerushalayim - when they are no longer performing a Mitzvah - no harm will befall them, how much more so on the way there!