Hand 1: easy fold

Hand 2: bet the turn. How likely is he to check a hand that’s beating you on this board, unless you’ve been v aggro. So many rivers you don’t want to see. I’d call a check-raise push aswell.

When you check the turn, you open yourself up to a bluff on the river because villain knows that you can’t check behind there with a big hand. Villain can’t really be value betting 45/56 on this river because it either looks like you had nothing/draw with you’re turn action and so you’re not gonna have a hand to pay him off.

So for me he either has the straight with 78/89/8xh or probably a busted flush. The chances he’s bluffing a busted flush go up because he knows you probably don’t have much and he knows that even if you have a one pair hand it’s gonna be tough to look him up because the river’s such a scare card.
With this reasoning though he shouldn’t need to overbet the river, but maybe that’s incase you had some sort of hand (JT?) and to convince you to fold.

So I’d go out on a limb and call the river as I feel he’ll have busted hearts enough of the time.

Hand 3: As someone else said, nothing has changed from turn to river. Again he probably would expect a big hand to raise him on the turn, so he probably puts you on a weak made hand or a draw,with a draw more likely.
He might be more inclined to check call with a decent hand on this river to induce a bluff from you. So I’d figure there was greater than a 1/3 chance you were ahead on this river and make the call.