Sending you a huge hug op. We were in your position 2yrs ago, very similar behaviours, nothing to do with teenage years, his behaviour had been challenging from 18m/2yrs I’d begged for help over the years from anyone and everyone, Hv, school, get set, camhs, paediatricians etc, everything was very unhelpful, getset did anger management with him, he would only go for the free McDonald’s, HV when he was little reassured me he would get easier, he didn’t. Camhs said your managing him well carry on doing what your doing and when he saw them in later years they just sent him on a self esteem group therapy course for 6wks.
He was under the paeds for 6yrs and they refused to do anything until he was older, then they would only do connors scale, repeatedly told me he’s not on autism spectrum because he makes eye contact(as someone who works regularly with adults with autism I couldn’t quite believe a consultant paed was peddling that crap, higher functioning people with autism can often manage eye contact) so no help at all.
School refused to do the necessary things to be able to submit a EHCP, it was such a big mess.
He had similar behaviour to your son, all the things you’ve listed and much more, except the hurting animals, he’s never hurt animals or set fires. He would often escape the house when younger, climbing out windows and scaling huge walls, often in his boxers and barefoot. He’d do things like climb onto community hall and run around on there knowing no one could get him down. He’d not come home at agreed times resulting in frequent calls to the police as he was missing. He compulsively lied constantly. He shoplifted from a young age, despite involving the police which at the time scared him, he stopped for a while and continued again when he was a bit older. He was frequently off school due to being excluded, on average 8days a month. It was unbearable constantly having meetings with school, having to collect him during the school day due to being excluded, I couldn’t have held down a job.
Sometimes we would wake up, both having felt that he’d been in our room whilst we were asleep, which was unnerving. For us it came to breaking point when he squared up to his stepdad after a dispute over a dvd and then turned and raised his fist to me whilst I was holding his baby sister. He went to live with his dad for a while, they had the same issues, he had to change school twice in a year, eventually we collectively called in ss to help, initially it was group meetings etc until a point came where he absconded from school and went missing for a week. When the police eventually found him they tried to bring him back to us, we refused to have him back, as did his dad and family, he was becoming a massive risk to his younger siblings due to his increasing violent and dangerous behaviour. The police weren’t happy when they rang me and said they were bringing him home, I said you can try but I won’t be answering the door, he’s not coming back here(felt awful at the time but knew it wouldn’t be an easy and knew we were at the point that if we pushed hard enough we’d get some help) his sw stepped in and said look we will take him into care but there’s nothing available at the moment, I was pushed into having him back, I thought that’s it were back to square one but she did keep her word and a placement was found, albeit a very expensive private one.
Since being there everything’s improved massively, he goes to a specialist school run by the placement, his behaviours improved but ultimately is more manageable with carers sharing the load so to speak. He’s finally got an EHCP, something I tried for years to get. He’s had drug and alcohol support, he’s had the YOT team involved. Every bit of help I’d tried to access over the years but came up against a brick wall he suddenly got because he was a LAC and they seemed to be able to put things in place which as a parent I couldn’t seem to access.
Our relationship is much much better, as his relationship with his siblings. We are no longer living in fear, I’m no longer stressed to breaking point, our house is quiet and calm.
He never did get a diagnosis, they wouldn’t go through with testing as he said he didn’t want to be labelled. It’s not about labelling though, it’s about gaining access to additional help, which as a parent is very hard without a diagnosis.
A lot of people will not understand behaviour like this unless they’ve been through it, it’s not as simple as limiting his PS4 time, it’s deep rooted, sometimes medical conditions are at play and it’s extreme and exhausting and I totally understand and empathise with you 
pm if you need any help or just need to chat