TPTK is great hand and the hand that wins the majority of pots in limit and NL. First hand it a bad beat. Only thing you can do is make 1/2 pot and pot sized bets to give your opponent incorrect odds to draw out on you. If you do go AI and put him to the test on a draw and he gets lucky, that's poker. If you had your money in the pot with the best of it than you can't feel bad about it.

Second hand: the min. raise tells you nothing. So you have to reraise or call the min. raise and bet big on the turn. The board is not threatening at all only few hands that you have to fear the piss poor K2/K3 or a set. You can rerise a serious amount on the flop and find out where you stand. If your opponent is holding a big ace ie. AQ, AJ you have him dominated. Maybe hes got A2 or A3? Just too hard to tell unless you pay for the info.

How you play TPTK depends on the texture of the game. What cards are your opponents playing? Online, I see a lot of people get whipped by playing marginal hands like K9 and Q9 b/c their kicker doesn't cut it. Also if they play goofy cards like 23 they can get lucky on flops like you described above. You won't know unless you play aggressive.

To answer your original question, you have to play TPTK aggressively. Don't check raise with it. Make your opponents pay for a draw. Watch the board. Are there flush or str8 possibilities? Are they all high cards that can easily make someone 2 pair? How vulnerable is your top pair to an overpair? Raise and reraise for information. If someone really tries to blow you out of the pot, you should strongly consider folding.

Finally, it is really weak play to put an opponent on AA or the nut hand every time. Watch the cards they show down. Did they limp from early postion? Did they raise big? Are they in a lot of hands or super tight? Lots of factors to consider....i'm rambling....hope this made some sense.