It ends if and when the child is adopted.
Generally, no.
no
Termination of parental rights does not terminate one's child support obligation.
Paying child support will not cause the father to lose his parental rights - neither will not paying child support.
yes, unless cleared by the courts.
The right to petition the courts for the right to see and support his child.
no not at all
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.
In this case even if both have agreed that the husband would relinquish his parental rights , then there is no need to support the child even in texas.
no