Yes. If the other parent has visitation rights the move must have the other parent's consent and the court's approval. The visitation agreement/order would need to be modified.
In some states, if the custodial parent moves more than 65 miles "as the crow flies" from the original address at the time of the custody agreement and does not get written permission to do so from the non-custodial parent, the court can (and sometimes will) remove the child and place him/her with the non-custodial parent. At that time the non-custodial parent will be given full custody of the child and even if the first parent moves back, they probably will not regain custody again.
With an injunction
yes..
Not at all! The custody agreement should stipulate how far away each parent can move from the other. Even if the non-custodial parent moved far away, they may still get time with the child. The worst that would happen is the custodial parent would be awarded full custody and the non-custodial parent would get visits.
Assuming the parent has custody, yes.
I'm assuming you are the father and a fit parent and then yes, you would probably get custody.
no see links below
They need to be modified. see link
No, unless a custody order is being violated, it is not kidnapping for the Father to move out of state with his own children.
Single mothers have sole custody, however I teach fathers how to stop such moves.
Unless there are unusually circumstances, once a minor becomes an adult under the laws of the state in which he or she lives (or as stated in the support order) child support ends. If he or she has established residence outside the custodial parent's home with the approval of the custodial parent, the obligated parent should petition the court to have the support order amended or rescinded. Child support money is for the support of minor children and not "owed" to the custodial parent. The custodial parent does have the legal right to sue the obligated parent for any arrearages or "extra" expenses incurred while the minor child was in his or her care.
No. The NCP must return to court to get legal custody and terminate the support order.