He will still have to pay support until/unless the child is adopted.
Paying child support will not cause the father to lose his parental rights - neither will not paying child support.
only if the child is then adopted
Yes, the right of a parent to be in his or her child's life has nothing to with whether or not he or she is paying child support. The court sees them as two entirely different issues.
Yes, because the father has no legal rights to the child. see links
child still need a father, late or not.see link
If he was not married to the mother, nothing until granted them by the courts. see links
The right to petition the courts for the right to see and support his child.
How does he have any visitation rights with a custody and child support order?
Termination of parental rights does not, in itself, terminate child support.
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.
Giving up parental rights has nothing to do with paying support. As the natural father, you are obligated to support the child the mother will be raising and can be ordered to do so by the court. You made the decisions; the consequences are yours. Think of the child and his or her needs through childhood. Would you want to be left behind because your father didn't want to support you?
Generally, no.