as far as stopping him from eating the floor, try to figure out why he's doing it. Is he bored? Is he teething? Is he getting all his minerals? Try setting him up with some raw hides and see if he chooses to chew those instead. If he keeps doing it, he's probably just learned to like the taste of floor. You'll probably have to start punishing him when he does it (squirt bottles are probably good). If he's doing it while you're not home, it might be a good idea to crate-train him so that he at least can only eat his crate

For the cat fur. Vacuum all the floors and every cloth surface. Dust properly (to get up the cat fur settled elsewhere) and then vacuum again (to get up any unsettled-uncaught cat hair). For things like couches and beds, clean what you can either in the wash or with something like Febreeze meant to decrease allergens.

Really, just vacuuming well is probably sufficient, but to make 100% sure, that will do it