I noticed a few things here. Firstly you need to remember that 15 hands is still a pretty small sample size. It's okay in that if you see someone open pretty much every hand in a 15 hand sample that they're very loose, so it's fine to believe he's on the loose side but I wouldn't consider those stats set in stone here. A 3bet would be fine here as I'm sure you'll get calls from worse, although if you're playing against someone who's really aggressive, getting 4bet here can be annoying. I'm not a huge fan of calling a 4bet with AJ even if we're in position so we lose a bunch of our equity with a 3bet at some frequency at the very least. Now onto the flop.

You've mentioned that this guy was very aggressive so first we need to realize that it's a little bit odd for him to not cbet here. A pretty disconnected board that isn't super likely to hit anyone and he checks. I think it's totally fine to check back there as our hand does not fair very well against a x/r and there are a decent amount of turn cards that can improve our hand. If he bet, I wouldn't be against peeling one time against this guy (though in all fairness, that can also be really bad as, hey, I'm not that good!). But when we do bet on a board that we would expect him to cbet, I think his x/r is a definite fold for us. I have no desire to play past this point, if he has a set then we need runner runner to win, he could overplay a marginal hand and lose value for himself and we just give it up and let him make the same play on a board that we have more value on. Or it could be a semi-bluff, like you thought it was. So not only do I think that he may as well just lead with the semi bluff, though x/raising is fine, the call doesn't work for us. If he's semi-bluffing then we're not super excited to see a 5, 6, 7, 9, T, or J. That's a lot of cards.

Now we DO improve on the turn to hands that can be beating lots of his range, and we raise and fold out all of it. What does he call with that we beat? What does he fold that beats us? Is he folding AQ that he decided to get tricky with? Or Q8 with his wide range?

I know its a long response but I think preflop is fine, so would be a 3bet. OTF I think a xb is much better than bet/call. If he bets I think we could at least consider a raise/fold line as well as a call. I think the turn shove is a clear mistake and as played we have to lay it down there.