I would just get it in flop given that he could easily have nfd+backups. you block his QQ some % of time and he should not have many 44,55 combos when defending BB. nfd+pair//2nd nut flush+top pair is good hands to put in gii range with QQ,44,55 for the balance purposes. Problem with calling is that you don't really have any nut outs. Btw, if you are calling otf, you should shove turn J as well. 

I don't really like getting that in on the flop in single raised pot. If u think that villian is that spewy to jam lets say 45xx + some gutters, then i think its ok. You said that he was fast playing his strong hands on flop, so depends more on how villian perceives strong ... but yea unless villian is that looose, in the better scenarios (for you) when you go AI on flop you will see pair + nfd. I think just calling IP might be better option, cuz we can see how villian reacts first on many turn cards + we can rep some of the runouts where villian might slowdown.

I would just call here.  Unless your opponent is really bad, it's hard to see how you'll get it in here much better than a coin flip.  While that's certainly marginally +EV, I think you will do much better by calling and playing turns in position.