1. Hard one actually. In the heat of the battle I'd call very fast, but thinking it over you are probably behind often. You beat 2 pair, but that's about it. but the nut flush...hmm...call.
2. It's good I think. Check calling with odds, or check/pushing could be alternatives. I don't know what is better.
3. I'd fold.
4. I'd call the 3-bet preflop against an unknown. QQ shouldn't be good enough to go all-in preflop.