Please don't deny he is the father if you're sure he is. If it gets to court and he gets his DNA results it will not look good on you if he accuses you of lying just to keep him out of his child's life or trying to delay matters. By all means put conditions on his contact due to the fact he was violent. Let him contact a solicitor or organise mediation so you can talk to him with a 3rd party if you feel able to. If not let him apply to the courts for a contact order and Parental Responsibility order, that way you can express your concerns about him having PR and get the conditions you want for contact put down in a legal document, ie. supervised contact for however long.
Because he was violent doesn't mean he wouldn't be awarded contact with his child though. And there is no reason a murderer wouldn't get PR of his child if a Judge thought it best on the day. Once he has proven he has his child's best interests at heart from now on, he will most likely be awarded PR by a court.
PR will not give him any extra powers over you as the person with the majority of care for the child. He should have a say in major decisions to do with the child's life but he cannot overrule you. If you disagree he would have to take you to court to overrule it and unless he has very good reasons, he wont be able to.
PR will not mean he can stop you going away. It is a very grey area because not all airports follow the same procedure but not many people actually gain permission from everyone with PR to go abroad and most are not stopped by anyone. Once again if he wanted to stop you taking the child away on holiday, he would have to take you to court.
Having PR would mean he can have access to the child's school and medical information. But again, he cannot do anything with it.
Having PR wont mean he can stop you moving. He can apply to the courts to try to stop you moving with or without having PR of his child.
If you have real concerns about him not returning the baby, especially any evidence with him suggesting or threatening it, you can apply for a residence order at the same time he applies for PR. That way he must return the child outside of his contact time.
It sounds like you could do with some legal advice about it all to pre-empt his possible court application. Good luck.