Final table with AK and short stack

[Lottery Larry]

A 22-player tourney, now down to the 6 cashing spots. The previous hand, I had AKo in UTG+1 and raised to T1700 to isolate a UTG all-in of T600 (blinds are T200/400), taking out his 97s (turn 9, river Ace) and putting us all in the money.

The next hand, I'm UTG holding AdKs with a stack of T5750. I'm the 2nd or 3rd shortest stack, with the three biggest stacks of 20K, 17K and 11K.

QUESTION 1: Does anyone raise anything but the standard 3BB here?

I raise to T1300, folded around to the BB chip leader. She calls, then bets 2K into me when the Jd4d4c flop comes.

QUESTION 2: Do I fold, call, or push here?

I didn't know a lot about her play. We had formed up the final table of 10 and lost 2 players in the first 2 hands. I was away from the table a few times, so we'd lost another player before I knocked out the bubble in 7th. I haven't seen her show too many hands down- she had been moved from another table.

She had some online experience in tourneys, so she seemed willing to push some chips around. If I was behind, I assumed I had 6 clean outs since she didn't reraise preflop. I didn't put her on a 4 since two were on board.

I agonized for a while, trying to decide if my T4450 was enough chips to wait for a better spot. I was 90% sure she'd call if I pusehd, so I decide to just call the 2K and see what the turn brought. I reasoned that my outs would probably be cut in half and I could more safely fold to what was most likely an all-in bet on the turn.

The turn is an offsuit Ten. She bet me all-in.

QUESTION 3- Call or fold?
Now I'm giving myself 10 outs (probably should have thought 8 outs, but I didn't think about the flush draw enough) and therefore my pots odds are good enough, and my prospects if I fold are weak enough, that calling seems best.

Thanks for the help,
LL

Oh, if it makes a difference:
6th place- buy-in
5th place- 1.5 buy-in
4th - 2.4 times the buy-in