Yes because it will tessellate
If a tile is a square or rectangle, cut the tile from corner to corner and you will create two triangles.
16
Not really...for tile to be properly set it must be on a hard surface. A carpeted surface will not provide the hard surface needed for tile to properly bond.
A regular octagon cannot tile a flat surface, it needs squares as fillers. An irregular octagon can tile a flat surface alone.
The rectangle is the simplest and most obvious case of a geometrical form that can tile a plane.
How long is the rectangle? If the rectangle is only one tile long, then it will take 20 tiles.
It is one surface on a rectangle.
Though people do tile over tile, it's really not recommended. The underlying surface can make or break a tile installation. Preparing that surface is the most important step. So I'd remove the old tile, prepare the surface properly and then install your new tile. This will insure the long lasting beauty of your fireplace tile.
Rectangle
rectangle
Before installing tile flooring, you need a clean FLAT surface. Tile is not a flexible material so the flat surface ensures the tile will match up correctly. You also need to sand the underneath flooring so that the grout and tile cement will be able to form a cohesive nature with tile and permanently fix the tile to the surface.
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.