Hand 1 - I would raise the flop over that weak bet. As played, raise the turn. You want his stack, not 10BB. River call fine.

Hand 2 - 1) if you're playing T8s from the button raise
2) raise more on flop, $4
3) donk over-bet on turn: this is often 2 pair, I guess sometimes stronger. I would just call, but I guess the min-raise bought you a cheap show-down

You're going to loose $$ with flopped 2 pair vs turned straight. You didn't loose too much.

Hand 3 - 1) If you're going to play TJ from the button raise.
2) fold the flop, you're drawing to a gutshot, the overs aren't very strong.
3) turn, raise more - oh, $2 behind, just push.

This hand is really a bad beat

Don't play un-suited connectors while short stacked. You need all the implied odds you can get with those hands.