So what did he take from you without your permission? Sorry if that's somewhere in your answers but I couldn't find it.
I've had quite a lot of experience with males of this age group and I would say does he go to the gym and do you have a chance of getting him into that/giving him a gym membership?
I'm going to suggest some things you can do. Please bear in mind that I am NOT saying that what you say to him is exactly what you think - I am modifying how you deal with him so you get the desired end result, and so that you humour him in some ways for now, while you both get through this very tricky year ahead.
My advice would be (and I know you will absolutely totally disagree with some of it, but with respect, what you've been doing isn't working well, so please maybe at least try this, much as it would be through gritted teeth!):
Knock to go into his room.
Go in quietly and gently, with some respect.
Do not now ever try to be hardline authority.
Go in and (sorry I know you'll hate this) - apologise.
Say sorry for being so harsh on him. And sorry for not understanding how he's grown up now and he is his own person.
Say of course you realise you can't police him using his phone - it's up to him. And his grades are also up to him. (so if he uses his phone and gets lower grades, that's his responsibility - but DON'T say that)
Say that when he gets angry and rude you feel really upset, because all you do is just to support him, and it's a learning curve for you too and you try to get it right. You are only doing it for him.
With chores, cooking, laundry, etc - I personally would just now drop the lot in terms of pressuring him. I wouldn't let him mess up public spaces but I would say ok I'll now be your support by providing meals and doing the house washing etc, and your job is to focus on your A levels and doing the best you can.
And I'd leave him to it.
And I would most definitely get him down the gym.
I might even say:
And so we start doing things differently, I think exercise would be a perfect way for you to chill out a bit and help you with your studies, sleep, everything. So I'm getting you a gym membership.
And then I'd get involved in sitting nicely down with him talking about what he's going to apply for at uni, his future, etc.
And I would NEVER in a billion years threaten to throw him out.
Never.
He's your son.
I know you have a super difficult and tiring situation with your younger son, and I am very sorry for that. I imagine it must be an awful ongoing 24/7 challenge and take a lot of your energy and focus. But maybe then just leave the older one to his own devices. I know probably the instinct is well he's older, he should help, etc, but it ain't going to happen. So just leave him to it.
He WILL grow up. When he's 22/23, if you're lucky. He will, but right now actually the focus should be his A levels and keeping all quiet on the Western Front, because you can't be fighting too many fronts at the moment.
I don't think you actually have a clue what being homeless is, or surely you wouldn't even refer to it.
I would rather live in fear of the police coming that have my son homeless.
And the 'fear' is only that you will have a clash with him that will result in him calling them.
To go to the police was an extreme move on his part. It was his version of a cry for help I think. So you need to DEescalate all of this. Not ramp it up.
Do you want your son to do as well as he can in his A levels, go to uni and have a good adult life?
Yes.
So change tack like I suggest.