How do I play this opening?

Just finished a game where my opponent played a variation of the Italian Game which is considered theoretically weak; but I was completely unable to take advantage of it and was reduced to an awkward position, eventually losing a pawn. Luckily my opponent made a mistake in the endgame and let me reduce the game to a rook-pawn endgame which was a pretty clear-cut draw.

I guess my main question here is, how should I play this variation of the opening (up to around move 7)? The exposed king is pretty awkward, and I'm not too sure that the bishop pair and pawn centre make up for it. Was there a good way for me to tuck away my king safely and take advantage of my development lead?

And to sum up some other questions which I have about the game itself...

Move 7: Was this the best square for the king to go to? Would it have been safe in the centre instead, where it wouldn't block the rook?

Move 11: I know this was a mistake, with an overeager pawn push. However, I knew there was only a brief window of opportunity for this idea, as the pin would soon be broken. Still, did I have some way of making use of the idea of attacking the pinned knight?

Move 15: Did I still have any advantage here? I have the bishop pair, but my development is awkward. Regarding the subsequent endgame, how should I have gone about developing my pieces?

Move 18: Did I have any way to make use of my advanced passed pawn to create promotion threats?

Move 25 or so: It seems I'm close to losing a pawn. Did I have any way to salvage both positional and material equality?

Move 29 onwards: Was I lucky in being able to salvage a draw while a pawn down, or was this pretty much a drawn endgame anyway?

Wow, that's quite a cool line...removing the defending pawn and then regaining a piece with a fork. I wonder if there are other continuations for White apart from 14. 0-0 though...still, it looks like the threat of the d-file rook is significant.