H1 - Cbet smaller. A minbet might even be optimal on this texture. You don't want to bloat the pot early and isolate the strong part of their range. J

T

9

is a very strong board. Two pair doesn't have crushing equity here. Ideally you want to see them just call, get a favorable turn, then put in the big bet. You can't really call a check raise IMO. They have the perfect range to barrel on you with straights, flushes, and combo draws. It will be so hard to get to showdown unless you hit a 4 outer. Yeah c-bet smaller. Face a much smaller check raise and proceed from there.
H2 - Going for fat value against their worse pocket pairs seems reasonable. The SB shouldn't have too many fives unless he's playing a ton of hands of pre. I don't think you're supposed to fold the turn like ever. They probably just have 22, 66 or a 5 though...