No he does not because he is not the child's parent anymore.
Paying child support will not cause the father to lose his parental rights - neither will not paying child support.
Termination of parental rights often does not terminate child support obligations. All it does is terminate the right to visit your child and have any say-so in their lives.
Giving up parental rights does not allow you to be free from the responsibility of your child. You may not want to be this child's parent, but you will still be responsible for the child.
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.
Generally, no.
no
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.
Termination of parental rights does not terminate one's child support obligation.
He is still the father with/without child support and has rights. Take him to court to get the child support and make arrangements for your move to a different state.