Playing an exposed card

[archcity]

Playing in our weekly NLHE tournament and I wasn't getting any cards. I am in middle position and the dealer accidently exposes my first card, and it is turned face up on the table Ac.

I say I would like to play card, no one disagrees so I get my second card when the deal comes around and it is another ace. Action folds around to me.

Questions:
1. Would you let a player do this in your game?
2. If a good card is exposed, say A or K, is it to my advantage to play it or just get a new card or redeal?
3. How would you have played the AA hand?