I think the answer to your question is about 33 percent presuming you are in a 10 handed game. But that is off the top of my head. There are probably some math people that can do the calculation in 10 seconds.
As for facing AA when you get KK, the odds of that happening are about 4 percent. But over the short term it can happen 50 percent of the time. Thats the beauty of the game. There are weeks when i lose with AA about 50 percent of the time. and then there are weeks when i win each time.
that full house question is missing a ton of variables. First off how many other people are in the pot, was there a preflop raise and how much, how do the other players play their hands etc.. If everyone limped in, then there is a decent chance you are up against a boat. But if you are heads up then there is a very small chance that you are beat. Not to mention the effect of raises on each player and what hands you think they would and wouldnt call with.
So if you are in a game and get this exact same situation you have to filter out a ton of variables before you can accurately know if you are beat.