Nut Flush x shove river

I think we can lead the turn when he checks back the flop. We could fold out some pocket pairs by the river and we can hit the river if he calls the turn. As played, I'm not sure what to do. He looks quite aggressive, so maybe capable of bluffing + I expect sets, A9, A3 and A7 to bet the flop. So, maybe we can call, but, from my experience, this move means the nuts more often than not. 77 makes sense.

I'd fold this, I don't think he's doing this as a bluff often enough to be +EV and even though he's argo, I don't see him doing this with a worse hand for value.

Only worse hand I can imagine him doing this for value with is Tc8c and that's a real stretch.

This is a very clear river fold.
To begin with, he is not bluffing. You look very strong when you donk this river so bluffing makes no sense. Even if he wants to bluff for some reason, he will just raise you and not shove (still fold vs normal raise because he's not bluffing).
You said he is aggressive and that means he will cbet his FDs => no worse flushes on the river. Even if he has one, he won't overbet shove something that is far from the nuts on this board.
It's always A7 or 77.

Are you attempting to x/r the flop? If so, it seems reasonable because a bet is expected here (what does it mean when an aggressive villain misses a c-bet on such a flop?). When villain fails to bet OTF I think we should lead the turn.

As played, villain's turn bet is too large to call. It will be obvious if the flush completes and there's little prospect of getting much more money OTR. You have pot odds of 2.1:1 and you need 4.1:1 (assuming your outs are all clean), so you would need to expect another $0.82 OTR when you complete for this call to break even. In the events which occurred you bet $0.90 OTR, so you would need villain to be guaranteed to call (and have a worse hand). Actually after rake I believe this line would be losing money even if villain is guaranteed to pay you when you hit.

As played, you should fold the river, unless you have a read that the villain is in the habit of bluff shoving the river. As a value bet, villain can only be expecting to be paid by flushes, so he must have a better hand.

We are x on flop to the preflop aggressor. What bet is expected here?
After his x we can lead turn.
On river we can x, but as played we can fold.

Clear fold on river, unless you have reads that he is crazy with bluffs. It will be FH like almost always if he is reg. Turn check is ok, you dont have to turn hand into bluff, bet is also ok.

You played that one really over tightly. You could've raised him pre, as well donked on the turn. There were several possibilities to avoid the final.