flush vs river shove

I don't think you can call here unfortunately. People don't raise OTF and/or call a raise OTT with only 1 pair before giving a decent bet OTR. I think you play against a very tight range here and your equity is too low. If villain checked it might have been a different story because you want to target hands in this case.

Push turn.
As played, you cannot call. Paired board, not nutted hand...

1) your opponent is capped
2) so, he mostly has weeak ace and small pairs.
3) XR on the flop is done mostly with 2p+, so that is what he does - XR + BET
4) Yes, i think you have to shove the turn. (you provided him the correct pot odds for calling with a set)
5) I don't think you should calling here bcs your opponent still could have AdXd. Fold

The pot odds (3:1) are good. Simply saying that "villain never bluffs" and "villain is not stupid enough to value bet AK/AQ etc" is making things too easy. It is close. You should take the matter to Equilab after assigning a range to him. (Well, if that range is 100% hands that beat you, don't bother, but such a range just isn't right.) You need only a little over 25% equity to call.

Push the turn. This river has to be a fold. T

he only combos we beat are weaker flushes and we still loose against nut flush which is definitely in his range.

Thanks, guys. I called and he showed A8. Now it looks so obvious that it was a fold. I hope one day I will learn.