The father, not married to the mother, has not seen his child (2 year old) or visited in over 1 1/2 years & has not paid court mandated child support in that time. There is also a restraining order against the father until 2011. Does he have any rights for child visitation now that the mother and child have moved out of state of CA ?

First, what has this got to do with child abandonment? Did you read the sticky note at the top of this forum on abandonment?

You can have the restraining order transferred to your new home area, which would preclude visitation.

The miother has full legal and sole custody of the child. Friends have called the mother saying that the father is going to get a warrant issued for her arrest because she left the state. Nothing in the custody papers said she could not leave the state other than that she had to inform the father before she left. She did inform the father by mail. What should she do now ?

If she complied with the court custody order she has no fears. The father is blowing smoke. To get a warrant issued the father will need to show she violated the custody order.