No they don't, as they don't have any body fluids. They're basically frozen in time, with no blood or anything running through their veins (i would assume there is venom?). This poses the question of how Bella got pregnant, but that's a whole other story.
I guess it's what sustains them? It actually keeps them undead. They're immortal but they can still get weak. It proabably gets used as energy and replenishes them, just like when we eat and drink.
No they don't because they don't have any body fluids and they'er basically frozen in time and they'er tollay dead so they can't drink, eat, or use the bathroom or anything like that.