2002 Chevy Avalanche Possible power steering or alternator

I have a 2002 chevrolet avalanche 5.3 liter. The power steering is going in and out. When at idle the power steering is not there. It seems to completely go away when the car accelerates. Also there is a problem with all of the power windows and other power accessories. When the power windows are engadged they go down normal . When i try to put them up my battery begins to drain quickly even when the car is on. This leads me to wonder if there is a problem with the alternator and if so, does this have any interference with my power steering. The belt is cracked but seems to be ok.