You're technically allowed to urinate anywhere if you need to (even in your mother-in-law's ear if you have nowhere else to go, lol [bechoros 44b]). As such, any style toilet in a private room exceeds urination requirements. (It permitted to urinate in public - bechoros 44b)
Single-occupancy bathrooms are preferable to multiple.
Berachos 62b relates a story of a multiple occupancy restroom. It's not proper to use one while someone else is, however it's allowed since it's dangerous to wait.
The requirement for where you can defecate:
- It is improper to go standing. Any ceramic-toilet with a seat fills this requirement.
- The toilet can face any direction. In an open field in Israel, one should not go facing east/west. In a walled room though, the direction of the toilet doesn't matter. (berachos 61b)
The bathroom should be far enough away that people can't hear you break wind.
Behind a fence one can break wind, without anyone hearing it (berachos 62a).
- At a minimum, the partition should block your sound. (Modern-stalls don't really do that.)
- The quieter, the better. For a multiple occupancy bathroom, a separate room for each toilet would be ideal, as each stall would be its own private bathroom, as opposed to standard-stalls, which sound easily passes through.
As long as the exposed part of his body cannot be seen, but the man can be seen. (berachos 62a)
- The height of the walls only need to cover the private areas, (if you are far enough away that you can't be heard).
- The number of sides would depend on whether people can see you on that side.
Normal walls which block the sound and sight are considered "far enough away" that you can't be heard, and therefore the bathroom can be anywhere within a building.
The area outside of the stalls in most multiple-occupancy bathrooms is not really part of the bathroom. The 'bathroom' is really only the stall with the toilet, and the room outside the stall has a different status (you can technically pray there if there is no smell). I don't see why there would be any requirements for the sinks and mirrors - other than the mirror shouldn't make it possible to see someone's private parts.