it is against the law to fold in a limit game

I think if your raising that flop you have to at he very least call the flop 3bet or you may start getting pushed arond alot. Alot of people will call your raise there on the flop with a king and raise the turn. Plus you are getting 11.5 - 1 which means you are not allowed to fold here ever.

I was railing when this hand came up. At the time it happened, I thought PokerPro made a good laydown. This guy was a pretty solid player. After thinking about it all night, I'm still not really sure what the correct play is.

I'm not sure what BB's range for 3-betting could be here, but I would think, AA, KK, QQ, JJ, AK, AQ, KQ, and a remotely possible 99 or 88. Of these hands we are WA/WB.

What do we do if we call the flop 3-bet and BB leads out when...
a. Turn is an blank or K
b. Turn is A, Q, or J?

Or, what do we do if we cap the flop and he leads out the turn in those situations above?

I don't think folding is such a bad play here. As Wota said, we are getting 11.5-1 pot odds, but I think we are in a reverse implied odds situation. If we are ahead, we aren't getting much more money in the pot, but if we are behind, BB will win at least 2 more BBs. Unless this guy is 3-betting PF and flop with AQ, 99, or air, folding is by far the best option.