Cats are usually less messy eaters than dogs, so putting down mats isn't a necessity. But cats do tend to sit in certain places, and mine leave cat-shaped hair areas. We cover our guest bed with an old army poncho liner. It ties on the bed frame, so the cats can't pull or jump it off. I can gather up their hair when I do the laundry, or shake it outside.
Cats do tend to want to drag their claws against nice, upholstered surfaces.
Sure, but as with most animal things, it's easier if you start right. When you bring your cat home, have something for it to scratch. A store-bought post, one you make, whatever. Use much praise when they claw there, of course. If your cat is already scratching the furniture or drapes, you can use a spray bottle with water to squirt them when they're doing it.