Why does the Torah insert the Parshah of Avodah-Zarah followed by the Zakein Mamrei, here? What is the connection between the Parshiyos?
Ramban: Because the Torah always begins a series of Mishpatim (punishments) with Avodah-Zarah or its worshippers. 1
Seforno: Having taught the Mitzvah of appointing Batei-Din in every town, the Torah now presents the Din of someone who worships Avodah-Zarah and of a Zakein Mamrei, both of whom are judged, not in their home towns town, but the one, in the town where he sinned, 2 and the other, in Yerushalayim, at the hand of the Beis-Din ha'Gadol. 3
Why does the Torah add the words "Asher Hashem Elokecha Nosein lach"?
Why does the Torah write "be'Achad She'arecha" - implying specifically Eretz Yisrael.
Ramban #1: Because that is usually where it takes place.
Ramban #2: Because it is only in Eretz Yisrael that the sinner is put to death by the gate where he sinned; 1 in Chutz la'Aretz, he is put to death by the gate where he was judged.
See Pasuk 5.
Why does the Torah see fit to specifically mention "Ishah"
Ramban #2 (citing the Sifri): Seeing in Devarim 13:14, the Torah precludes women from the Din of 'Madi'ach', it needs to teach us here that they are included.
Which covenant is the Torah referring to?