Hand 1, their ranges should be pretty wide. This is about 20 percent QQ-: JJ-44,AKo-ATo,KQo-KTo,QJo-QTo,JTo,AKs-A2s,KQs-K8s,QJs-Q8s,JTs-J8s,T9s-T8s,98s-97s,87s-86s,76s,65s. According to Flopzilla, that hits the flop 40 to 50 percent of the time, depending on whether they're going to call you with 66 and below.
Your options are: check calling. Check calling doesn't make sense here because you want to charge the draws and maybe fold out very low pockets.
: betting. If you bet, they fold probably around 30 percent of the time, (If each calls 45 percent of the time, they both fold .55*.55 or approximately 30), plus you are obviously calling the HJ if he ships for 50 more, so you'll get to realize some of your 20-25 percent equity. Estimating how often HJ ships and the other guy folds, approximately 25 percent of the time? 30 percent they all fold, 35 percent of the time HJ ships, let's say it gets through 70 percent of the time... So 30 percent all fold; 25 percent you call HJ; 45 percent you get called by two or raised by the deeper player or called by the deeper player. Let's say you lose when that happens... (obviously not true, you could catch A or K or they could be on a draw and just check behind, but just for sake of argument.)
So EV=.3*255-.45*140+.06*445-.19*190=4.1.
OK, so hand 1, check-folding and betting is probably about the same, dancing around break-even. I would bet, but I'm a total spew monkey in these spots...
Hand 2 is trickier, because he never folds better except maybe 22 and 33. 88 and 99 have a draw, and TT+ is too good to fold for most people. It's hard to know what the best line here is in terms of EV, because we don't really know his range, we don't really know if he's going to bluff with KJ here... What we do know is that he very likely folds AQ/KQ/JTs if you bet... So I'd just probably bet-fold 95 or 100. If he ships on you, you can fold. It's pretty close, but against JJ-55,AKo-AJo,KQo,AKs-ATs,KQs-KTs,QJs-QTs,JTs,T9s,98s,87s,76s, if he ships overpairs+ and OESD, you only get 19 percent equity... If he's wider pre, it's a bet-call. Basically, I don't know, but I feel like overall, with the different possible ranges he could have, bet-call is still probably pretty close to break-even, while bet-fold should definitely show a profit, even if he's only folding hands that you already beat.
I'm not good enough to go for higher EV by catching bluffs by missed overcards, with A high and SPR of 1. So I don't mind betting 100 and him just folding KJ so we can move on. It's theoretically bad poker, but show me a clearly better EV line and I'll take it. If we were up against a very straightforward player, check/folding and then betting the turn if checked through is likely much better. But with short stacks and a player who's capable of making a move, I would just bet-fold. I don't think he'd bluff shove KQ for 137 more, and you'll probably win that pot with 1/2 pot bet more than 33 percent of the time.