I am very new to PLO so def take this with a grain of salt but I think the flop call is fine and I don't think you need to bet.  Turn call I think is good too, there aren't a ton of terrible river cards for us and we block some of them.  Also, If we raise/get it in on turn villain probably has us beat or excellent equity vs. us.  Hands that just call our raise are probably not putting more in on the river when behind very often, and if those same hands can check/call a river bet then checking may become more profitable.

You gave no reads, so we assume these are unknowns. Though, you have more than 100bbs, so you must have played a couple of hands and at least know if the BB is reggish.

Assuming the squeezer is somewhat reasonable, he most likely has good high cards, good aces ss or double suited high rundowns. On the flop, when the agg checks, i think it's a reasonable spot to bet with our TP+ gutshot, it looks strong and we make them fold a good chunk of equity. If they raise we are never really bad. A check might also work, with the plan to raise if Btn bets. But i'd prefer to bet in this spot.

On the turn, his bet looks on the weak side. We should also consider that the Q hits our range better than the initial aggressor, so his bet makes me believe he is more likely to also have a Q in his hand plus some high cards. That means a lot of equity against our hand. We don't like a 7, 3, A, K, also 9, on river.  That's about 25-30% equity, we are happy to fold out if we raise in this spot. We don't let him realize his equity. Yes, it does look like we have a draw when we just call here and he might pay on river, but i think this will happen less often then the benefits we gain from him folding out the equity in turn. Additionally, we keep our range more balanced when we have a solid combodraw on turn and decide to raise.

This is my opinion, please post if you see it differently. 

Thanks sorry forgot to say this is Zoom but had some data that 3bettor is decent so most likely high cards/aaxx type of hand. Agree with the flop analysis, should probable bet here with many hands, including this. Turn still not sure but see your reasoning. Anyone else?

I think that I cbet flop and considering that he likely has AAxx I doubt that I ever fold (would need a read to say other wise).  Too many turns that we can play well, and it's really hard for him to x/r AA here.

Turn I think is a must raise mainly because the Q really improves a bunch of his 3b range to worse hands that he will probably bet call (OP+GS, wraps, TP+OE).  Also hard for him to have TTP with his rundown/broadway hands since he missed the flop cbet.

Bet flop, he may fold AA no draw, and if we check we are in a close spot if btn bets. I dont love c-ring vs him unless he is a stabber or aggro.

Turn: a decent player will play well vs a turn raise, but like ppl said above, a A/K/T/7/3 puts us in a gross spot. A Q/J/9 will prob kill our action a lot. There is a benefit of calling def, its deceptive and he is more likely to pay off a river bet with 1pair and a hand that wouldve folded to a turn raise. But theres really only a few cards where we may be able to reap the benefits: 6/5/4/2 so i think id just take my eq and raise turn.

If you want to strengthen ur range by calling turn, you will still have some Q7xx and potentially QQ and lower sets that arent so vulnerable that u just call turn with, and will be able to extract some value otr.