I don't know the dimensions off hand but it's probably smaller than you would expect. It's a really nice piece of furniture, but I didn't like the same when paired with my living room entertainment area. It looks great in a bedroom though.
I wouldnt see why not as long as its a solid surface not carpet, though the have magnet doors so it might be an issue to push the the on top open might slide.
I wouldnt see why not though they dont give instrctions on how to mount. My guess would be drill through the back into studs and you would be ok as the shelf it self is heavy.