Chumley was a VERY bitey cat when he first came home. We dealt with it like we did with kitten teething. We'd blow a short, sharp puff of air directly in his face (that totally startles them) and say "no." We'd explain - you don't bite people (I know, sounds nuts, but we talk to our cats). Then we'd slowly reach out the hand again (try reaching in a fist). If he goes to nip, blow again, say no, and get up and leave him sitting there.
There's three things about this: I assume he's biting when you're petting him? If so, he's being overstimulated - but that means that redirecting to play isn't necessarily the best option. If this is the case, you need to work on finding his limit. Pet a few strokes - give it a pause - pet a few more strokes. Yes, he needs to learn "no" and that biting people is not OK - but it's also best to learn his limits and avoid overstimulating him.
But always praise the heck out of him if he shows you other ways. When Chumley switched to just putting his mouth on us but not biting down at all, we praised that. When he went to just move his head like he was going to bite, but didn't even put his mouth on us, he got even more praise. Now when he's nervous, he'll bop us with a paw, no claws. WHAT A GOOD BOY!!!!!!!!!!!!!!!!!!!!!!!!!!!
(That's what we tell him.
If he's biting because he wants to play, then redirecting to a toy and praising the heck out of him for playing with the toy is absolutely the right thing to do.
Cats do GREAT with praise for the right stuff. Knowing what's good and right is SO important, and goes a long, long way to altering the behavior.
The only "negative" modifier should be the short, sharp puff of air directly in the face. People don't hiss too well - but that puff of air they definitely understand.
But the bottom line with this one is that kitty has to learn that "inappropriate" behavior gets him ignored, not "rewarded" with negative attention.
So - is it play or overstimulation? If play, redirect to toy. If overstimulation, work on finding his limit, and not going beyond it, but don't let him get away with biting. Teach him "no" with the blow/puff, and if he pushes it, he learns he gets ignored for "bad" behavior. And praise the heck out of him for good behavior, he needs to know what's right.
As to the scratching... several of our kitties "bury" their food.
But they just paw around it... is it maybe that his claws are so long they're getting caught in the carpet?
Sounds like maybe you should put something down on the floor under his dish... a rubber mat? I know you don't need to spend more money on him, but a welcome mat at Walmart is pretty cheap, and might help save your carpet.
Also, as to the scratching... they generally like to scratch and stretch when they wake up, so placement is important.
Whether that's vertical or horizontal is a preference of each cat. And surfaces are also kitty preference. Cardboard is a favorite around here (though they sharpen their claws REALLY quickly on cardboard
) - and we have the slanted one, and horizontal scratchers in cardboard. We've tried vertical sisal posts - but they're just not into them. The do love the vertical sections of the cat trees (carpeted) - but they don't seem to confuse that carpet with the carpet on the floor.
Billy's the only one who scratches on the carpet - and that's because he loves to nap in the hall, and that's where he scratches.
We just spent $20 on a recycled rubber door mat - really long (for like a double door or something) - that we're putting down there so he stops destroying the carpet.
You can also sprinkle posts/cardboard scratchers with a little catnip to help attract him to them.
But inappropriate scratching.... really the only way to stop it is a combination of "benefit denial" as I call it, and providing nice alternatives.
As to the food burying... for Tuxedo he was such a nut about it, we took Hissy's advice, and set his bowl down on a handkerchief. That way when he's done, he can scratch the handkerchief up over the bowl and feel like he's accomplished the job.