I would have bet flop in both spots.

#1, if you haven't been 3betting him much at all and he does decide to call, you have to really assume he's doing it for set value most of the time. I mean, it's not like you have a reason to believe he's calling the 3bet w/ the intention of messing with you whether he hits or miss. Your range should appear strong in his eyes and this flop sucks for pairs. If he does happen to peel one you have 10 likely outs, plus he's more likely to c/b the turn which will give you another free card often.

By the time you make your A on the turn you can just bet/call it off and not have to worry about being bluff raised or semi-bluff raised.

#2, definitely definitely bet the flop. He's limp calling, he has so many weird random hands in his range. Besides, when you are OOP, you've got to bet to define your hand. If you don't do so, it forces you into precarious situations like the one you are now in on the turn--he's raising and you have no idea what it's with. If you bet the flop and are called, it doesn't at all mean he's holding a king, there's a ton of value in betting here.