AK in 3-bet pot

I would say yes to fold, unless we have some strong read.

What kind of hand would call preflop and shove turn? I guess middle NL5 opponent will just call with AQ+ OTT IP with FD. I think it is fold most of the time - your opponent do not represent anything than JX, also your line pretty strong 3B => 1/2CB => 2/3 CB.

Because it is an all-in situation, you can also calculate this. You just need to put his range into the equilator and see if you have the pot odds to call

He is basically repping the jack here and nothing else. I don't know which jacks he's calling the 3bet with preflop, that kinda depends on the type of player. I guess BTN vs SB he might call some suited jacks in position. But if it's the type of player that folds AJ and all other jacks here, he is full of it. If it is the type of player that likes to call suited jacks here because the hand looks good, he's going to have a lot of jacks in his range. But if he is that type of player, he will call all sorts of hands preflop and his range will be wide overall.
So he is repping a hand he can't have (because he folds all jacks but JJ preflop), or I think not a very large part of his range (only the hands with a J in it). Well that doesn't say he has it or not. He could very well have a jack if he calls it preflop.

But why raise the turn and not the flop? The Ace is already on the flop. So if he really has a jack he's probably going to think I have a jack and he probably has an ace, so let's raise it now and try to get it in. But meh who knows what these people think. Maybe just slowplays it 1 street. But I'd be kinda suspicous nonetheless, and if I would fold I would keep an eye on him.

Well we will face more stronger hands than draws here so fold is ok.

Villain is on TT-22 and suited connectors and one gappers, 99 and J9 are likely. Hero has two outs. Fold.

You can take a note that villain raises turn with non nut gutshot and low FD when the board is paired. That is quite weird move imo.
Very often you will face stronger hands here and I would just fold turn without 2pair+ if we don't have reads.