A: Child support is something that is, in essence, never final. If they can show that there has been a susbtantial change in circumstances since that original order, then that is enough for the court to revisit the issue. However, the court may do nothing, or it may rule in your favor. Modification, as it is called, is very fact specific,. I would advise consulting a good family law attorney in your area.
A: If there is no order in place, the North Carolina has not yet asserted jurisdiction. When you're talking about custody issues across state lines the Uniform Child Custody Jurisdiction and Enforcement Act (UCCJEA) is controlling. Under the UCCJEA North Carolina would be the state of initial jurisdiction. Which means that if the father filed for custody after you move to Florida, you could conceivably be required to come back and appear at a North Carolina Court proceeding. At that point a determination would be made as to what is in the best interest of the child, which very well could be for the child to be in Florida. But judges can be unpredictable. You could also file for custody once you got to Florida. Florida would have jurisdiction to enter a custody order, however unless and until the child resides in Florida for a period of six months, then North Carolina is still a home state, and would still have first say as to where the custody action must be maintained.