Sure. It will taste a little different, but fundamentally, the main thing is the acid - you'll just get some extra flavor (which you may or may not consider an improvement) from white wine, cider, red wine, rice, malt or balsamic vinegar, rather than white.
Absolutely, the vinegar is just providing the acidity. Each vinegar choice will alter the flavor, but that could be either good or bad. Experiment and see what you like and you'll have your own sweet and sour recipe that is like no one else's.