On the turn, Pretty sure you are beat at this point and are drawing to 2 pair/straight. Also, he could be potting with some overpair plus flushdraw hands which you aren't in good shape against. You aren't getting a good enough price to draw out and you are likely behind so just fold.

In regards to raising the flop. It would be nice to know how much villain is 3betting in this spot to get an idea of his range and if he is one to cbet 100% in spots like this. My standard here is a call though.

Turn is an easy fold. Not sure why you feel priced in. You have 21% vs KKxx/AAxx/Ace-high hearts without a pair/sd. You're absolutely crushed (13%) vs. a hand like A789 w/hearts.

you have nothing so why would you go all-in. At these levels and up to 100 PLO plyers don't bluff a lot, so unless you have a real good read on a guy you should just play your hands fairly straight-forward(with good starting hand selection) and you will make money..