size?

Yes, I did without hesitation, but I also but a layer of 2" stone on top of my bottom board. (6) 16" pieces worked great on a 36" x 48" bottom and I grouted it all with masonry grout in the regular caulking tubes.

Yes. But you should buy one large enough to allow for some space between the heater and the edge of the pad, so it doesn't overheat it.

Yes, it can be used over carpet. Ours is 3 ft X 4 ft.