#1 - b/f flop, pretty much give up if called
#2 - 4x preflop, I don't get the flop min raise AT ALL. If you really think your implied odds are good enough to draw to a gutshot opening up the betting round again just gives him another chance to give you shitty pot odds. Him donking 0.06 does usually represent a weak made hand/ draw though just call and play the turn IP.
#3 - PLAN YOUR HAND! If he's that short on the flop then it shouldn't be that hard to get the rest of his chips in on later streets. I feel that raising only commits you more and folding is too weak. I'd flat and reevaluate the turn.
#4 - I think calling preflop was fine. When he bets $0.06 I'm inclined to think he's weak. Either c/r to $0.15 on the flop or flat with the intention of leading "good" turn cards (yes the 2 was a good card). Why the hell are you drawing to a gutshot against a shortstack without the intention of stealing the pot the majority of the time?
#5 - FLAT IT AND REEVALUATE IP ON THE TURN