First hand (KT): As 'rilla said, this is an iffy call preflop. Sure it's only a min-raise, and if you'd already paid the .25 then paying .25 more isn't bad. Cold-calling any raised pot with KT usually is a bad idea though. Take note that this guy doesn't raise much preflop with a fairly good hand - most people here will tell you that JJ is a limp or raise big situation (I'm a fan of the latter).

Your play on the flop was fine. Calling his all-in when that J hit on the turn was absurd. You have at best 5 outs if he has just one J. Since he had two, you were drawing dead. But even assuming he had one, calling here is a bad idea. He stayed in for some reason after your flop raise. It's quite possible that he'd have played like this having TP-ok-K or a middle pair. When the J led him to raise I'd be confident he has your tens beat, quite probably with two pair or better.

Second hand (AA): Preflop play = good. 5xBB is a good raise. His call here was obviously a huge mistake on his part, and I'd be noting it so that if I saw him again I'd be ready to take advantage. When the flop came, your raise was very weak. Sure you don't put him on low crap. Still, there's a str draw on the table, and since an Ace could be involved it in, it's more dangerous than mid-range str draws (as many people at this level will call a preflop raise holding Ax). Bet half the pot or more and make the chumps with A3/A5 or the idiots with 35 fold. Bet stronger on the turn here too, since it didn't impact the str draw. Remember, even if AA is the best starting hand, if you don't hit, it's only top pair. You gotta make people pay if they want to try to draw out.