Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Nate is biting and scratching aggressively.
From your write up it appears that he has always been somewhat aggressive/mouthy but things have recently worsened. This may be part of the reason that he was put into a rescue situation.
Since this has ramped up whenever we see a change in behavior, especially when a normally easy going animal becomes cranky, it is worthwhile to look for an underlying health problem. None of us is at our best when we don't feel well.
If he is healthy on physical examination, and a stool check, mini blood panel and urinalysis check out fine then this may be purely a behavioral issue.
If that is the case then there are some things that you need to think about to help you solve this issue with Nate.
In what context do the bites occur?
If you've been petting for a while, even if it seems short to you?
Or is he stalking you and biting/pouncing on you?
You may not know this but it would be helpful to know at what age he was taken from mom and his litter mates. 8 weeks is a perfect time to leave mom and litter mates. At that point mom should have taught him some social niceties and his littermates should have taught him not to bite down hard.
But if he's very energetic and you use your hands or feet to play with him he may be forgetting his manners.
And some very pushy cats get irritated when they don't get their way and respond aggressively.
So we need to teach him that people aren't for mouthing ever.
Start by no longer using your hands (or any body part such as feet) to play with him.
Use toys, especially fishing line type toys that he can chase and burn some energy with.
If he does bite you yell "ouch" and then walk away and ignore him, play over.
If he continues to attack he's likely overstimulated. Use a towel to scoop him up and put him in a quiet "time out" room.
And set him up a little.
Walk down a hall, let him start to chase but once he goes to pounce have an air horn ready and give it a blast. That isn't directly related to you, but it is to his actions. And if it happens every time he will get the idea this is no fun.
You can also use a squirt gun in face or the air in a can that you can spray in his face.
It does need to happen every time he misbehaves though or it will take longer to stop this behavior.
Never try and discipline with your hands. He is already overstimulated and he will just get more excited and bite harder.
He may find your hand clapping to be a stimulus and think it is part of play behavior, so I would discontinue that, since it doesn't appear to be working anyway.
This is a pretty common problem in very active cats, especially Siamese or oriental breeds and their mixes as they tend to very "oral" cats.
Do expect him to get a little worse before he gets better if his biting is related to play behavior as he is having great fun and won't want to give up his games.
Some cats get overstimulated by physical attention/petting.
And when this happens they will bite. They don't mean to hurt you, they are just saying "stop!" the best they can.
It is important to read the cues he gives before the bite to avoid it.
It's likely his pupils will dilate (enlarge) or he will become tense or his skin will "crawl". If you see or feel that than stop and you hopefully won't get bit.
I would also keep your petting sessions very short with him.
Best of luck with your fellow, please let me know if you have any further questions.