Child support and child custody are handled separately. In most cases delinquent child support payment does not affect the rights of the father. The father can still petition to avoid you moving the child out of state but, doesn't necessarily mean it will be granted. Unless both parents can come to an arrangement/agreement in what's in the best interest of the child.
no
No. Your obligation to support your own child takes priority over any subsequent support you offer for another person's child. The court would not decrease your child support obligation for that reason.
NO!
no
yes
no
Generally, no.
Yes, it can. Moving in with the other parent is grounds for "flipping" child support payments. However, this must be done by court order.
Yes
no
Child support needs to be decided on by the court. In most cases, the noncustodial parent is responsible for something. If the custodial parent makes considerably more than the noncustodial parent, monies many not even be exchanged. To resolve this issue, it is best to file papers at your court house.
The court will enter a default judgment against them. Better to show up and have a say in what is going to happen.