no
To fight for your rights see links
I don't believe so.
The father might seek visitation and/or custody.
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.
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).
no see related link
Yes.
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.
He has the right to petition the courts for visitation.