Some kind of connector or suited Queen is playable. Check the flop for pot control - try and get them to think you have AK and missed. Betting this flop is only semi-bluffing with 2 outs to Aces Full. You could hope for a Jack to hit, and then bluff it strong.

This is a tough spot, but you really shouldn't go broke here. If he has a straight draw - then he's in good shape, although Aces aren't outs for him. If he has any lone Ten or a pocket pair, it would be hard to outdraw your AAQQ.

You really shouldn't show strength and alert him to your holding. In case, he decides to charge you the premium on each street to showdown. Check the flop since it doesn't hurt your hand.