Usually would fold preflop. I don't remember how I played this at those stakes though, so looser than I'm used to may be okay.

Fold or raise on the flop. If you think his raise is bs (it was only a min-bet, so depending on the player this could indicate a good hand, a poor hand feeling out the competition, or nothing at all), then reraise! If you think he has a king, you're all but throwing your chips away.

Should that have read SB folds? How can the BB raise and fold on the same street?

Fold the turn unimproved, especially to this big bet. Given the action on the flop, it's possible that you are ahead here, but you have no way to know that enough to call a bet. I could see an argument for betting here, but certainly not for calling someone's all-in.

River advice above me is G00t.