Which Shevu'ah is the Pasuk referring to?
Ramban #1: It is referring to the covenant that Hashem made with Yisrael at Sinai, when He declared "ve'Atem Tih'yu Li Mamleches Kohanim ve'Goy Kadosh!"
Ramban #2: It is referring to the covenant that Hashem made with Avraham in Lech-l'cha Bereishis, 17:7 "Lih'yos l'cha l'Elokim u'le'Zar'acha Acharecha" 1
Ramban: Which He will reiterate later in 29:12.
What are the implications of "Vehalachta bi'Derachav"?
Refer to 11:22:3:1-3 and note.
Lev Eliyahu (Sh'mos p.78): It refers to teaching Torah to the people, just like Hashem teaches Torah to Yisrael.
Shabbos, 13b: It is a Mitzvah to emulate Hashem's Midos - 'Just as He is Gracious and Merciful, so too, should we be gracious and merciful!'
Oznayim la'Torah: 'If you will also adopt Hashem's Midos, 1 He will establish you as a holy nation - but if you merely keep the Mitzvos, He will merely raise you above all the nations.
See previous answer.