There isn't a picture so I can't be sure, but I have seen stone "rugs" in a number of rooms so it's possible.
I believe this is the 'rug' you are referring to? I don't see why not. I shared your question with SoPo Cottage as well: http://www.hometalk.com/571827/create-your-own-bathroom-rug-in-stone-glass-or-marble
Here is another idea
and tile in the kitchen is the best.
Absolutely! I've never done it in a room that large, but I don't see why you couldn't put a 'rug' in the kitchen. It would look great!