1) Raising preflop here is fine, limping is fine too. Depends on the table - the looser the players behind you are the more inclined I would be to just limp - AJs plays decently multiway and I don't fancy the idea of playig a raised pot with AJs OOP. At a table of unknown's it's close to 50/50 though. So preflop is fine.
2) Lead the flop. There is absolutely no reason not to. Trying for a check-raise is reasonable too (even if it's checked around you aren't too worried about giving a free card as you have the strongest draw out there)
I guess part of the reason I felt weird about making a raise on the flop was because I had the nut flush draw, and if I he pushes all-in over the top or something, which seems pretty commonplace at this limit, I have to abandon it, whereas if I just call, I know I get to at least see the river.
You should not be afraid to take the pot down as soon as possible, as opposed to having to play the rest of the hand out of position having handed an opponent the initiative. Your hand is strong, but not strong enough to 'slowplay' like this OOP. Check-calling the flop is going to leave you with a really awkward turn decision just like the one you had to make the vast majority of the time, as to villain it probably looks like you have JJ or something and are scared of the Ace, so he will bet with a large range of hands that you are beating, but similarly can have a lot of hands you are not.
4) As played, well, as I said you've left yourself with an awkward decision. $24 to win ~$68 with one card to come, so you're getting not far off 3:1, you're just over 4:1 to hit the flush with one card left so villain doesn't have to be bluffing often for the call to be okay (and this isn't even factoring in implied odds when we hit the flush, which probably pushes it to break-even without even considering if villain may be bluffing or betting with a lesser hand). The thing is though, if you miss on the river, you're probably going to be faced with an even tougher decision.
Probably call and fold to a sizeable river bet (or check behind if he checks) if we miss is the best course of action. Obviously if we hit we can bet/shove depending on villain's action.
Edit: Actually it's a pretty clear call, rereading what I've just written. It's still not a nice spot to be in, though.
Edit II: storm, dbitel is correct. What exact part of "how the hand was played" is encouraging you to fold? It's around about a breakeven call even if villain is bluffing or betting with a lesser hand 0% of the time, which cannot be right (Harrington's 10% law etc).