As far as the pets go agree with PP, rehome. As far as your DS behaviour goes the answer is a little more complex. My DS lashes out in meltdowns, there can be a point where it becomes outside his control yes, I've seen him completely out of control, been hit, headbutted, kicked. Ive also seen him use the situation to hit out, it felt like he was giving himself permission to lose it.
It's one thing as a child, a completely different matter as he grows into a teen and an adult, he could do serious damage. It's unlikely the premise he can't help himself is completely correct. With the right support over time and hard work, involving you as well as him, I expect he can be taught to recognise when he is getting overwhelmed and use strategies to stop himself from getting there, remove himself front the situation, seek help. He can learn to recognise and avoid/minimise triggers. He can learn strategies to help keep himself calm. There are likely points before full meltdown where he can step away. There are things he can do if sensory issues are at play. One strategy I'm working with DS on recognising when he's had enough, which he's starting to voice now.
It's a long term process, but it can be and does need to happen. At some stage you or someone else may get seriously injured if he continues to believe it's ok to hit out because he can't help himself and then never tried to help himself. I'm teaching my boys that even if you can't help yourself in the moment you're still responsible for working on not getting to that point.
I'd get professional help from a psychologist if you can afford it. Maybe school can provide some help. If you can't access any professional help you can still work on something like zones of regulation with him.