Don't they just beam it out?
That's my understanding, yes.
Nah, I think that's just way too futuristic (in a silly way). Just because they can doesn't mean they do. I can imagine that they don't use toilet paper but bidets throughout (the future will be Japanese!). And to save water, although that won't be a problem either, it's probably some kind of sonic bidet. In one episode we've seen Bashir using a laser of some sort to sanitize his hands before surgery. That's the way it is in Trek.
