stains on the windows, or windshield? Some degreaser products can stain the windshield if they're left to sit. Not sure how you would stain your windows. Are you sure they aren't fine scratches? a lot of times when people don't wash there car very often they get dirt in the seals and when you roll your windows up and down it can scratch them.
There are some acid products on the market that may be able to remove them, but these are products you can typically buy OTC. Most detail shops will have them though. I can't remember the name, i'll have to ask the guys in my detail shop what it is called.
The black plastic vinyl that turns white can be a pain in the ass. Most products you put on it will look like they took care of it, but as soon as they dry it's white (faded) again. If you can find a product called "insta-shine" get some of that and spray it on the areas that are white. Don't whipe it down, just let it sit. That'll take care of it for a while. The only real solution though is to have it re'dyed.