hand 1 depends on opponent imo. not sure what stakes youre at, but micros, id be checking back here most of the time OTF, then Vbet turn/river. people who have a clue (starting at 25NL and higher) will often bluff c/r this flop w/ air because an ace is simply a tiny part of your button range and you cant really call without one, so ye.
hand 2, i like bet flop, check turn, bet (or call the donk bet) river, cos youre getting calls from like you said, AT, AJ type hands, as well as 66-TT OTF. lots of vils esp fish interpret your checking back OTT as you had air OTF and consequently will donk the river for bwtween half and like 80% assuming theyre getting a fold. i often find myself hero'ing A high in these spots sucessfully.
hand 3a, i like your logic. bet flop, check turn back unimproved on any card but A and see a free river (if vil c/c's flop they generally are OTT too)
3b, bet flop always/raise donkbet. look for pot control OTT. i prefer betting flop and turn as opposed to flop and river here for obv reasons. youll often get value from AT+ and underpairs, and turns going to be either J+ imo good barreling card, or <7 in which case i like check back, eval on river whether you can Vbet
EDIT: just saw youre on 4NL. ignore my fancy ace air c/r for hand 1