I would continue raising but stronger to make them fold more frequently after their limp. With that line, you reduce the positional advantage of BTN and you take the lead (a Cbet on many dry flops will have lot of success). And villain will have to adapt his limping range by making it stronger (or by ORaising more often with some hands which were before in his limping range), so he will limp less often but call (or raise) more often (after his limp).

I would definitely check, it's not like 4 years ago when people folded 60%+ versus a cbet and small pp are usually pretty bad hands to start bluffing with. In the same spot i would definitely raise a suited connector which often make a great bluffing combo.

Ok. I prefer check when there are at least 3 other peoples in the hand (less FE preflop and more implied odds postflop).
So what are your checking range (small PP and ?) and your raising range (SCs and ?) here ?

I don't see a lot of benefits for raising, I would just check preflop and try to hit the flop.

i think it depends on stack sizes and opponents. in a vacuum, i just check 22 every time.