[Triumph36]

I haven't read the other responses.

In Hand 1, A flush card on the turn slows both of you down since neither of you can put the other on a non-flush draw. The board is otherwise drawless. If you like to play dangerously and think he might be testing you, you could call the flop min raise and go for a turn check raise. But if he checks the turn and a heart falls on the river you will hate yourself. I like raising a little less than the pot here - he's not laying down a set, and if he's fishy enough to min-raise, he might flat call with a flush draw. Don't get tricky - I find that min-raisers are usually terrible, and he either has garbage, a flush draw, or a huge hand. The latter two will pay you off and the first one won't put much more money in.

Hand 2 - I think a 7 or low pocket pair will use this min-raise. I'd go ahead and call it and then check raise any turn - who semi-bluffs a flush draw on this board? If he has a bigger jack you're paying it off, he's too short and possibly tilted not to. But you can easily commit him to an awful hand that way, rather than three betting the flop and letting him get off easy.