Noob warning - giving my feedback more to be told why I'm wrong than to really help you

Hand 1:
He's out of position, so must be sure of his PF hand. I'd put his range at TT+, KQs+, AK, AQs or maybe even more narrow. I'm mostly inclined to think he's holding an overpair. A made flush is unlikely because you have As and KsQs is the only suited spade hand I see in his range. He could be holding AxKs also. I read his bet as a semi-bluff and I'm leaning towards push - I don't think it's too much of an overbet. He'll probably fold, and if he doesn't you have 9 outs to the nut flush (assuming no straight flush). It would be a stretch to put 5s5x or 7s7x in his range, and I'm not buying it. Actually I'm not sure I'm talking sense. You called a 3-bet he'll only fold if he thinks you hold something that's made or beating him. You have the As - you could in theory have a second ace or a second spade and he should fear that. I wouldn't expect him to accept that you've called a 3-bet with a low pair (set) or suited connector. High suited connectors are of course possible - unless he has them. I think I'll stick to my guns and suggest push.

Hand 2:
I'd tend to put a good amount of pocket pairs and suited connectors in his range due to your comment and his stats. He could well be sitting on a lower set, a made flush, maybe two pair (65s), and overpair with a spade in it. I'm not confident in this one, but it is rare that folding a set on the flop is right. Calling is almost certainly wrong as you don't want his hand to improve further if it isn't made. I'd probably go with a healthy raise as you're ahead of a good part of his range. I'm sure the people who know better will tell me my range is too wide and you're actually behind, but there it is.

Hand 3:
He's loose and it feels an awful lot like he's playing 65 (probably suited). It's what he wants you to think which makes me a bit suspicious. If he makes the straight on the turn is there any +EV in him doing c/r? What hand can he think that you would have that you would call with? Is he semi-bluffing Ah2h or Ah5h hoping for the fold? I'd probably buy his story and fold. The only alternative I see is if you have enough of a read to think he's semi-bluffing in which case even a push gives him odds to call (he has $13 or so left after his raise). It's probably a fold.

Hand 4:
I can see where the set thought is coming from. JJ might be in his PF 3-bet range though. With you betting the flop I can see a set would be happy to call to let you put more money in the pot on your own initiative. Since he's responding to a heart I guess the question is if we can put any suited hand in his range. Preflop, yeah - on the flop call, maybe less so. AhJh is possible. That would give him TPTK with a nut flush draw and would have played this way. 98s or T9s are probably out. I think AhKh would also have folded. Could be JhTh or KhJh too I guess. I don't see any straight draws in his range, or any two pairs. If we limit his range to sets (not JJ) and 2 hearts of which one is the J and the other is T+ that gives us 3 possible 66 hands, 3 possible 77 hands, 3 possible TPGK+ with flush draw hands. He's overbetting it a bit, so your pot odds are bad. As a whole it looks like a fold to me. Even if a stone-cold bluff is possible it's unlikely enough that if you put that into his range you're probably still behind.

Hand 5:
Ok, he calls a 3-bet and he's nervous about the flush draw so puts in a near-pot size bet. I see AK, KJ and JJ in his range for sure. Or a flush draw as you said. You're effectively putting him all-in so he needs to call $16 for a chance to win $59 or so. I'm not sure you're enough ahead of his range that raising is correct. I don't see any real future in calling here either. Maybe fold is in order.