You need to talk to a lawyer to hammer this out. Theoretically you can be required to pay child support but also not have visitation rights; it depends on the custody arrangement you have with the child's mother. If you don't have a custody arrangement, then the lawyer can help you set one up.
You can sign your rights away but you will still have to pay child support if you are the father or mother of the child. There is no way to avoid paying child support.
Paying child support will not cause the father to lose his parental rights - neither will not paying child support.
If you're the father, and the mother is attempting to deny you visitation rights, you need to get a lawyer and take it to court. If you're the mother, and you'd like to deny the father visitation rights, you need to get a lawyer and take it to court. Child support is an entirely separate issue. It has NOTHING to do with visitation or custody rights. You are obligated to abide by the court orders in both cases, but you don't get to stop paying support or deny visitation just because the other parent did the other one of those things.
If the father has visitation rights and the mother refuses to allow the father those rights, then the father can sue the mother in a civil contempt proceeding. If she doesn't have a good reason for disallowing the visitation then she can be held in contempt of court. There are various remedies including giving the father more visitation to make up for the visitation that was disallowed by the mother or even giving the father custody, but usually, the judge will just order the mother to allow the visits. His paying or not paying child support has nothing to do with whether or not he gets visitation (i.e. he gets visitation regardless of whether or not he is current with child support).
You can take it to court but if you acted as father sometimes you can owe anyway because you accepted that role.
No.The only way that rights can be terminated for that purpose is if mother remarries and step parent legally adopts.
Even if he is paying, he has no rights until court granted.
If you mean, what are the Dad's rights, he has the right to continue paying child support and the right to visitation, both as established by the courts.
if the mother terminates her rights can he collect child support from the mother if child lives with him?
An unmarried father cannot "choose" to not pay child support. The laws in every state require that a father pay for the support of his child. The mother must bring an action to the appropriate court so that a child support order can be established. Visitation rights are separate and a father can have visitation rights established by the court. Visitation rights are not dependent on paying child support.
Relinquishing parental rights does not terminate support; however, generally, adoption does.
One does not mitigate the other, so it would be up to a judge to grant both requests.