Yes.
If you have sole custody no. However, can you still provide for the child? School etc? If she wants to prevent it then let her go to court.
Yes, if he has visitation rights or shared custody, she will need his consent.
Yes, but the father can still file an injunction to prevent it.
Doubtful. The child support is for the welfare of the child, not the mother. Check with your state child support office for specifics of the law in your state.
If he has court ordered visitation and pay child support she will need his and the courts permission to move.
Technically, yes. It does throw a problem into the mix though -- now the mother not only has to go through the state to get to the father, she has also placed another state into the picture. Now the mother has to petition the state she moved TO to petition the state she moved FROM, both of which have different custody and child support laws and two separate agencies. It would be much simpler to postpone moving until she has petitioned the original state. The less government involved, the better.
In Wisconsin, if you are not married to the child's mother, you generally have the right to give your child your last name, but the mother may have a say in the matter. If there is a dispute, the court may intervene to decide on the child's surname based on the best interests of the child. It's advisable to consult a family law attorney for guidance specific to your situation.
DO NOT ever pay child support to the mother or the child. Pay it through the courts or the State Disbursement Unit.
The State of Texas child enforcement agency would have it. Sometimes it takes a couple weeks to get to the mother. The state would still have it if they haven't given it to the mother.
the best defense is to have some physical documentation stating that you are indeed the father. once you have this get a lawyer to argue before a judge that this move would not be in the best interest of the child and due to physical constraints you would not be able to be a stable presence in the child's life which you strongly desire. this is after you are proven to be the father and have a custody agreement.
States do have laws against it, as well as it should have been addressed in the custody orders, but you should immediately file an injunction ordering her not to remove the child from the state pending a full court hearing on the matter. see links below