In carved stone, there shouldn't be any chemicals or toxins. At least, as part of rock, they shouldn't be coming away (people typically carve out of hard rock, so that will diminish wear and tear). There really shouldn't be anything to worry about.
As for the surface, rough is helpful. Cracks and poc marks/small holes is even better. Moss is a non-vascular plant, so water can only move through diffusion. This limits the size moss can get, and also somewhat where it can grow. On a rough surface, a drop of water will stay much longer, and not dry as fast. If a crevice gets wet, it puts the water slowly to the rock surface until it has all evaporated. This can give moss growing there many times more water than the moss on flat rock is getting (check out this image, where the moss has only grown where it had sufficient water).
On a glazed surface, even if you artificially add water, so the moss could grow, it will have a hard time attaching to the surface. However, many lichens will grow on non porous surfaces and moss can use the lichens as a foothold. It would be easier to use a non porous, especially somewhat absorptive material to grow the moss, and make sure it gets wet every day and stays in te shade.
Moss Can thrive on concrete, just like on natural stone. Look for the same characteristics in concrete as you would in stone. The care of the moss is identical. If you are casting your own concrete with moss in mind, mix 1 part dry peat moss or finished compost to 2 parts concrete mix. This will hold moisture better, and moss thrives on it. (I did this with pavers one time - strong enough for foot traffic).