On your first question, 11...Bxg4 is not tactically sound due to the simple 12. Bxg4 when the only way to not drop a piece is 12...Nxg4 13.Qxg4 Nxd4 but then white has the powerful 14. 0-0-0! with a strong attack once the knight retreats. Therefore it might be better to try 12...Qb6 with the idea of taking on b2 after the bishop retreats, offering some compensation for the piece. 11...Nxg4 is not better though. For example 12.Bxg4 Bxd4 13.Bxd4 Bxd4 14.Bxc8! with some interesting complications which are nevertheless favourable for white.
However, 17...Rxb2! is correct, as you suggest, because if Kxb2 then Nxe4 gains basically all the material back with a strong attack to boot.
I dont have an engine on me, and I need someone to check my tactics in the following game...I was black: