What is the significance of the Bris mentioned here?
Seforno: If he will go in His ways, Hashem will be His G-d and the G-d of his children, 1 whom he will teach to go in his footsteps.
What has the Bris Milah got to do with the promise to give Avraham Eretz Yisrael?
Rashi: The promise of Eretz Yisrael was contingent upon the Mitzvah of Milah. 1
Which explains why Yehoshua circumcised the entire generation that was born in the desert before beginning the conquest of Kena'an.
Why is Bris mentioned 13 times in the Parshah?
Rosh (verse 13): This corresponding to 13 Midos through which the Torah is expounded. Bris, Shabbos and Tefilin correspond to the entire Torah.
רש"י: ברית של אהבה וברית הארץ: אולי הכוונה רק לברית אחת?
גור אריה: כיון שסַתם "ברית" ולא פירש איזה, יש לפרש שהברית ניתנת לו לכמה דברים.