OP my heart is breaking for you, you sound so miserable and at the end of your tether.
But please do not give up on your son. The fact that nursery think he he is great is a good thing. It does suggest that the problems at home can be fixed, as he does not present with them at school.
Your priority is to protect your daughters. Being woken in tears and in pain every night will be having a deep, profound and long lasting effect on her and it needs to stop NOW. Put your son in your bedroom with you, he needs to feel loved as right now he probably feels like the most unwanted kid ever. Put a tall stair gate on your bedroom and put your baby on the landing if need be.
Ignore your sons bad behaviour. You say it is weird that he pretends to scratch the car and destroy things, it really is not. At his age they are all about pretending and imagination but instead of being a super hero, he is consumed with anger and jealousy and so that is manifesting as destruction. He has learned that the only way he gets attention is to be naughty or even to pretend to be naughty. Get him an Amazon kids ipad, they are guaranteed for two years no questions asked and it will help to give him focus and be something just for him.
Also, you really need to enforce boundaries desperately. Not just with him but with all your kids. Children throve wit strict routines and firm rules. They do not want to sit at the table? well that's tough. Mine all sat in high chairs, then at the table until they were 13/14. So get the two youngest highchairs with trays and you and your son have a seat each. Or get a folding table and chairs for in the living room. Ask your son to help you chose dinner, butter some bread, anything so that he feels like a big boy that is getting to do something that the other two are not allowed.
You can get through this. Just start looking for solutions instead of problems. You need to separate the kids, you can do that with stair gates.
You do not have 3 bedrooms, so get a folding bed in the living room or a single day bed that looks like a sofa with a trundle underneath it. Then you and your OH and baby can sleep in their. Your son can have his own room as he is desperately in need of some space of his own, and so is your daughter.
If you 100% can not do that then consider a partition wall in the biggest bedroom with a stair gate to separate them so they both have their own space.
Make easy food choices. Batch cook when the kids are asleep so you can just reheat or buy easy cook food like pizza, ready made meals and supplement it with lots of fresh fruit and veg.
Try and cuddle your son as much as possible. For no reason. If you see him going to do something naughty then divert him with a tickle fight and pepper his face with butterfly kisses. give him the attention before he is naughty to try and break the cycle.
His behaviour sounds like its learned. I am a mum of four and had something very similar as my kids were very close together too. You can do this.