Flop is fine, I think he ships it with a set. Unless he's being very tricky, only you know if he's capable. I doubt it though with the flush draw there.
Turn, you gotta call man. I don't think he has AQ (no raise pre - again only you know if he would usually raise with this hand pre?). He wouldn't raise with just a6 or a7 on flop (usually). If he has Q7, fine, but I think it's more likely Axhh or 67.
Fold pre-flop. I am working on this myself as it is too easy to tell yourself it's only a dollar but it puts us in some marginal situations. Also, if we don't connect on flop we wasted half a big blind to "see a cheap flop". I think this is a big leak I have and may be something to think about in your own game.
I don't think completing here is terrible pre flop if you know the villain and can make the right fold at the right time.
Basically you're getting like a billion to one, and if you're a good player and can manage these situations, it can end up profitably. This hand, case in point.
CAVEAT: only very good players can do this! I don't claim to be one, but on a weak table this CAN be profitable!