What must they learn?
Rashi: They must believe in Hashem (some texts - convert).
Malbim: Hashem will exile the nations and Yisrael amidst them in order that they will learn from Yisrael true Emunah, when they are exiled and humbled like them.
Why did Hashem say "bi'Shmi Chai Hashem"?
Radak: From the time that Yisrael returned from their exile, they did not serve idolatry or swear in the name of Ba'al. If [the other nations] will learn Yisrael's way regarding this and this, this is Bitul of idolatry!
Why does it say "Ka'asher Limedu"?
Radak: Yisrael learned to serve idolatry only from their neighbors 1 .
The Erev Rav made the Egel, and Yaravam similarly made golden calves, which Yisrael later served! The Torah warns not to leave the Kena'anim in Eretz Yisrael, lest we learn to serve their idolatry (Shemos 23:33)! Perhaps these are included in Yisrael's neighbors (the Erev Rav were mostly Egyptians). However, these are not connected to exile of the nations around Eretz Yisrael! And Achaz learned from Ashur, and built a Mizbe'ach just like the one in Damesek, to serve Elohei Damesek (Divrei ha'Yamim II, 28:23)! (PF)
What is the meaning of "v'Nivnu"?
Rashi: It is an expression of building.
Radak: Many converted when they returned from exile and dwelled among Bnei Yisrael. They have Binyan among them, i.e. endurance. Yonason translates like this.
