1. Fold is good. To go into a bit more detail here, when I was learning NL ring, I thought this was an automatic, routine fold here preflop and that's really not the case. Seen as how the lower stakes still play relatively passively, you are fairly new to NL ring lean heavily towards just mucking pre. You can get into some tricky spots, high variance spots here both by cold calling and 4 betting (of which, against 2 agressive players, I heavily favor the 4-bet... keep in mind that a range of AA/KK/AK here is ahead of KK). Anyway, to be clear, if button has a tight range here, this is always a muck preflop if you're even reasonably deep stacked. 100bb eff easily applies here.

AK is a nut hand here sometimes at 100bb deep, eg if lagtard is getting out of line here, make it $20 to go and call a push. Pushing yourself is another option.

2. I don't know. Logic says fold. I think I would call here sometimes. I might even raise here out of spite sometimes but I'm not really sure if that's as a bluff or for value.

3. unanswerable. Put BB on a range and figure out the best way to play post-flop. As a default, I think the raise on the flop usually sucks because it lets him play perfect poker against you. I think I let people have a look at 6 overcard outs here too often in the interest of protecting my stack.
unanswerable. Put BB on a range and figure out the best way to play post-flop.
4. I really don't like this flop raise. I think a call is best but if you're going to raise, I'd want to put real pressure on the guy. As played, I'd probably just check behind on the turn. Getting raised off your hand sucks, and if the guy called the flop with a king or better, he's obviously never folding. Ok, now that I realize that you DID get pushed at, you have to fold. Unless you think he's going nutso with a combo draw then you can call him. I put him on something like KQ here a lot.