What should play white?

Well why on earth would you have played 12. ng5 if you didnt want to take the bishop on move 13?  13. nxb qxb 14. bg2 (practically forced given the threat of ng4) qd7 15. b3 and white has more space.  Black pretty much has to try to play for f5, so play might continue 15. ... ne8 16. e4 and the immediate f5 runs into bh3 so black has to wait.  The computer likes white's position a good deal but doesnt seem to have any real ideas to make progress so I suspect its pretty close and the computer is over-valuing the space a bit.  

F4 - what does it do positive?  What it does negative is give black some squares for his pieces, leave the e-pawn backwards, and open the dark square diagonal.  Computer says its about equal after f4, but its just a funny looking move.  

is that bishop stronger than my knight?

move 13 Nxh3 Qxh3 Bg2 Qd7 b3

worth noting that black D6 pawn is backward so at move 13 after Nxh3 Qxh3 Nb5 could have been played threatening to take the pawn and in turn you would have a potential passed D pawn