1)
Why did He say "Ki Amartem Hekim Lanu Hashem Nevi'im Bavelah"?
1.
Radak: This that I tell you that I will redeem you after 70 years, is Emes. However, you say 'Hashem established for us Nevi'im in Bavel who tell you that you will return now' - this is nothing. They prophesize Sheker to you.
2.
Radak citing Targum Yonasan: "Nevi'im" are teachers.
3.
Malbim: "Bavelah" refers back to verse 14, "va'Hashivosi Eschem El ha'Makom Asher Higleisi Eschem mi'Sham Bavelah." Ki Amartem Hekim Lanu Hashem Nevi'im" stands by itself; you were exiled because you say 'Hashem established for us Nevi'im', i.e. you believed the false Nevi'im.