1)
What do we learn from "v'Yashevu Aleha la'Vetach"?
1.
Malbim: When they first returned, they had haters and people who pained them, like it says in Ezra and Nechemyah. Afterwards they built houses and dwelled serenely; the settlement of Eretz Yisrael will increase.
2)
Why does it repeat "v'Yad'u Ki Ani Hashem"?
1.
Malbim: They will know that I, Hashem their G-d, oversee them with Hashgachah Pratis special for them.