#1. You should raise about .08 and should be done with the hand. Depends on how often the BB has tried to defend his blind. The guy on the button should most likely fold as he was probably just trying to see a flop for cheap and that will get him out of the race. Although at the extreme micros, it is very likely he will still call, even with complete air just hoping to hit. So bet, but be cautious if he calls then bets out on the flop.
#2. I don't think you know what the definition is for min bet, because if you did then you would know that you cannot bet lower than that unless you are pushing all-in and don't have enough to cover it. I think what you are meaning to say is that when the guy re-raised you, he didn't make the re-raise 2x your original raise(therefore, when you bet .08, he didn't make it .16). When I see that, you can view it in a number of different ways. If it is a aggressive opponent, he is probably trying to throw you off a hand, so you should go ahead and 3-bet him. If it is someone who is tight, you might want to get rid of that hand. You find these smaller bets a lot at the micros for a couple reasons...
1. People don't pay attention to what they are betting, they are just thinking(well it's more than that guy bet, also why you will sometimes see someone re-raising the original raiser like .02 more.)
2. They are trying to bet the least amount that they have to that they think will throw you off a hand, because they don't want to sacrifice any of their precious micro bankroll.