You need to take the mother back to court to enforce the visitation order. You should act ASAP. The mother is in contempt of a court order and if she continues to ignore the court she could lose custody.
no
To fight for your rights see links
The father might seek visitation and/or custody.
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).
1) to pay support; 2) to petition the courts for visitation
If you are not married the custody automatically falls on the mother and the father have to go to court to get visitation or custody. If you are married you have equal rights.
She has to be served. see links below
Generally, no. However, you have not provided any detail and there may be circumstances under which an unfit mother may lose custody to a step father who has been a stable parent to the child. You should speak with an attorney who can review your situation and explain your rights and options.
No. Not if a family court has jurisdiction over the child and the father has visitation rights. If the parents were never married and there has been no court involvement or paternity established the mother can try to move. However, the father could file an action in court to establish his paternity, visitation rights and prevent the removal of the child from the state.
You do not have the right to deny visitations but if you do, the father can and should request a court hearing to establish his paternity and get visitation rights. He can request custody or joint custody and the court will render a decision. If the child is to remain with the mother the court will set up a child support order and the father can file contempt charges if the mother withholds visitation or violates the visitation order in any other way.
He has the right to petition the courts for visitation.
No. You would be signing away your rights to visitation. A parent generally signs away their rights in preparation for a legal adoption.