pre is ok but I would make it larger lik $0.12 at least if I decided to play. Checking this flop multiway is pretty bad since you are giving loads of gutters a free chance to catch up + you rate to have the best hand a good % of the time. Check/raising this hand is very bad. When villains min-bet, their range is usually polarized to extremely weak hands and extremely strong hands. By check/raising here, you get all the super weak hands which you crush to fold and all the hands that have you crushed will continue.

When he comes back over the top which part of that range do you think he has?

It seems you did not consider his range at all. Practice putting him on a range, it's the only way you will learn.