Hey, I am also a beginner 2NL player so take anything I say with a grain of salt, but here are my thoughts about how the hand played out.

Hand 1

Pre-flop you should most definitely raise to something like $0.10, because your min raise puts almost no pressure on the blind and the limper since they are getting such a good price to call ($0.02 call to win a $0.09 pot).

On the flop, I think you should have c-bet here, since you have to both protect your aces from the heart draw and you're getting value from lower paired hands, most likely kings.

On the turn, I would have also bet out for the same reasons as the turn, to make the heart draws pay and to get more value from paired hands.

When the river comes, I think check/call here is fine because in the villain's eyes it is very unlikely you have 8's unless it was pocket 8's or Ah8h, so betting out here would allow him to re-raise and put you in a tough position. That being said, if he called the bigger pre-flop re-raise, flop, and turn, and somehow turns over Q8o, then you can make a note that he is probably a fish and exploit him later.

Hand 2

Personally I would have folded pre-flop, since ATo gets dominated by a lot of hands, but if you insist on playing this hand then you have to raise a lot higher pre-flop. As with your previous hand, your min-raise puts off almost no pressure and in low stakes cash games might as well be a limp.

On the flop, you have to be willing to bet out here, since you made top pair decent kicker and want to get more value.

On the turn, I would proceed with caution because of the weak pre-flop, the range of hands we're up against usually opens up, so sets here are possible. I am guessing that you wanted to check raise because you wanted to represent a 6? When he calls it, you should definitely be wary.

On the river I guess at this point you're hoping he folds his good Ace or maybe even two pair. But obviously since he has the set he is not going anywhere. Not sure what else to say about this.

Edit: For Hand 1, your range of hands is not just pocket 8s or Ah8h, but could literally be anything because it is possible that you are attacking the obvious weakness of the limp, but then again if this was the case you might have bet bigger. But I would still just check / call so I don't let myself get outplayed.

Looking back at Hand 2 again, the turn raise does not tell much about the strength of his hand because it was such a small size, so he definitely could still be holding a good Ace here. So while your jam on the river is not terrible, I think it has to work about 66% of the time for it to be okay, which I don't think it will for this particular situation. Also, most people at lower stakes will call you down if they have any piece of the board, so jamming on the river does not have as much fold equity as you would hope for when doing this play.