questions from Stud/8 newb #8

[Truthiness24]

#8.

20/40 Stud/8, 5 handed

I have no useful read on Villain except that she seems solid. She's played about 4 hands when this comes up.

I bring in for $5 with (A8) 2, 2 diamonds.

Action folds around to the last player to act, who has (XX) A. She calls $5. Pot is $21.

4th:
Hero (A8) 26 -- calls
Villain (XX) AT -- bets

5th:
Hero (A8) 269, 3 diamonds
Villain (XX) ATT

Villain bets, I fold.

I made these presumptions about the hand. Can you tell me whether they were wrong, and why?

a. She didn't raise on 3rd because she wants me to catch up just a bit so that she can bust my low. She's leading me in to give her hand more value. (Or, she played it weak.)
b. I can put her on aces up or 3 10s a whole lot of the time.
c. In any event, I'm behind even the pair of 10s and I'm drawing to half.
d. Without a viable way to win high, I can't continue. The pot is too small.
e. The call on 4th was kind of loose. (How often would you call 4th here?)

f. What if instead the action was:

Hero: (A8) 2, 2 diamonds -- BI -- calls
Villain: (XX) A. bets

Pot is $61.

4th:
Hero (A8) 26, 3 diamonds -- ???
Villain (XX) AT -- bets

Now I've caught "perfectly" and I'm still only drawing to 1/2. I'd need 2 diamonds or some other craziness in 3 cards to even beat a pair.

I can't imagine that villain is bluffing after catching a 10 on 4th. (Can I?)

Is this why this kind of hand is subpremium? How often do you muck this on 3rd? Would it be the right play to fold 4th?