Stop and take a step back.
Yes this manshape is a vile twat. However, you liked him enough to mix your DNA and produced your baby. You both are the parents of this innocent child.
Regardless of your current personal opinion of each other, you will now always be connected due to this child.
Even though babies can't speak they are still impacted by what is going on around them. Please remember this for your interactions with him especially around the baby.
You need to cultivate a business relationship with him, keep things formal, keep everything written down and be professional like you would with a despised colleague.
He is angry and maybe scared, he will be telling his mother whatever it takes to put you in a bad light. That is his choice and its something you need to keep replying to his mother, calmly, that X and I are Y's parents and we need to discuss this together.
The maintenance is a CMS issue, let them deal with it. It is not linked to contact, he does not need to pay to see his child.
The courts if it gets there, do not care about your wishes and feelings, they will not care about his either, they put a plan in place for you two to stick to that is supported by the evidence available with a starting point of 50/50 which is then adjusted based on age and other factors. Because you are both incapable of working things out as parents together.
None of this excuses his behaviour. But you cannot choose that, you can only choose your own reaction. I would send a letter, asking to meet with him in a neutral location, I would set out clearly that overnights are something you want to work towards but I am concerned with how you were with the nightfeeds. Use lots of I statements and keep them bland and professional.
It will be awful, it will be upsetting, but you have to be strong enough for the child you created together. Explain to him that as he didn't attend the registration and you are not married that he is not on the birth certificate. Let him explode, keep yourself safe, and if he starts shouting simply respond, I can't hear what you are saying when you shout, it scares me and its just noise and teeth. If he won't calm down then say, I know how hard this is but we need to calm down for our baby, let me know when you are ready to talk, and then leave. Keep yourself and your baby safe. Follow up any conversation in writing like you would take minutes at a meeting.
Good Luck