H1 - I would just call her turn raise, not jam.
Reasoning - she's repping a hand like JT, 44, or 22. Her bluffs would be flush draws or some ace-wheel combo that might be a combo-draw. She might also have a hand like 98s or KQs that picked up a flush draw.
Our hand has equity to improve against JT, is drawing dead against 44/22, and way ahead of her semi-bluffs, which we want to keep in.
We have removal to JT, which helps narrow her range a bit. She might not raise JTs from EP, and there are only 2-3 combos available. Likewise, she might not raise 44/22 from EP, and there are only 6 combos. So her range here is likely pretty weak compared to our hand.
When we call her turn raise, she's either going to give up and check to us on the river, or continue to barrel. We can fold if she bets huge on a card that completes her most obvious draws, but call on a brick. If she checks to us on a brick, we can bet thin for value, or check back. If she checks to us on a card that completes a draw, we can check back.
H2 - harder to do the hand-reading here, and harder to know what to do. This is where the reads become more important.
As the PFR and OOP to two opponents, I think it's better to start with a check on this somewhat dry flop. We can check-call a bet, or even check-raise.
Here, I'd be check-raising at some frequency, depending on who bet, and how much. If she bet small, I'd be very likely to x/r. If the MP player bet big, I'd be more likely to just flat call, especially if she already called.
Her raise over the MP caller is pretty strong. She's repping 2P+, in a spot where her most obvious semi-bluffs can just flat call IP and realize her equity.
The 3d on the turn is basically a brick, other than adding the BDFD. Her bet sizing is a little weird, at just over 1/2 pot. I'd be thinking she has a hand like J9dd or 97dd, hoping for folds, but giving her draws a good price to chase. I'd think 2P+ would want to go for a larger sizing.
The stack depths here are awkward. When you jam, she's getting 2:1 on a call. If she thinks she has 15 outs, she's getting almost but not quite the right odds to call. In theory, your jam should fold out all her draws, and only get calls from 2P+.
Alternatively, if you just flat call, the pot will be $900, with $650 back. If you know she's capable of jamming as a bluff, I'd think she'd be jamming the river a lot if we check to her, no matter what card comes.
I think I'd just flat call turn, with a plan to block-bet any river card for a small size, like $150. This will put her in a tough spot. She can jam for another $500, but she'll be laying you better than 3:1 on a call, in a spot where she could have a lot of bluffs that get looked up light, and her made hands could be behind.
She'll probably just fold her bluffs, and flat call with all but her most nutted value hands. It'll be hard for her to raise, even with T8, when we could have AA, TT, 88, AT, A8s, A3s, etc, and we're unlikely to be turning JJ-KK into a bluff.
We'll lose some value by not letting her bluff, but we avoid having to call off a jam in a spot where she's pretty polarized to 2P+ or nothing.