You can min/raise ... just have a good reason to. Folded to on the button with 56s is just not the right place, because you
a) probably don't have the best hand (not for value)
b) aren't really building a big pot (although you are in position, so good)
c) are not betting enough to bluff/semi bluff (you would rather they fold a random hand than play it vs. 56).

With KTo, maybe a m/r on the button is better vs. terrible opponents.

As for the flop call - no read is so good that he NEVER has a J here (don't forget 77-AA are all possible ... although I would assume QQ+ reraises preflop) - I mean he is exactly representing that he has a J. But the options are not J or 2 or 3. He could have any pair, or a flush draw, or A and a gutshot.

In any case - It's not that bad.... I just think your reasoning might be out of whack.