Villain here is 34/8/25 but seems to have trouble getting away from good, but not great hands in the face of resistance. For instance, she PFR one limper, got called by Button and limper. Flop came [Td][7s]. Action went, check, pot bet, call, min-cr, call, AI, call, before it got back to her and she couldn't get away from Jacks. Anyway onto this hand.

I limp UTG, she limps behind me ($29 - I have her covered). Blinds see the flop.
[Jd][Qd] Pot $2
check, check, I bet $1.50, she calls, blinds fold. I'd pretty much been invisible at this table. Can't say what my image was if she was paying attention, but I was definitely not over-aggressive.
Pot $5
I bet $4, she calls.
Pot $13.
She has $23.50 left. I take a while and then throw out a $16 bet. What does she need to call here?

Bonus hand (because I don't want to start a new AA thread).
OTB [Ah] $47.50
UTG min-pfr to $1 ($14.50 left)
UTG+1 calls $1 ($30.65 left)
UTG+2 calls $1 ($38.20 left)
CO calls $1 ($59.30)
There is $4.75 in the pot already. What's the best play here? $6? $10? What about a push even?

#2, enough so that the guy with the biggest stack would be making a mistake to call. So at least $7. I like $8-$10.

#1, nowhere near enough information. If I were you I would be putting here on a bare or and would expect her to fold, unless she's dumb enough to think a rivered top pair is enough here. If I were her ... well, I can't think of a hand I'd play so passively here unless I thought you were a donk.

Little more information. She has [Tc]. That takes one of the cards you think I have away. Enough to call that bet?

I probably call the river with [Tc], yes. You could have flopped the flush but a flopped set and KQ type hands are also possible.