It sounds like you want to use the threat of refusing to allow the father to see his son in order to pressure the father to pay child support. That is not how it is done. If you want to go after him for child support, get the courts to order a garnishment of his wages (or other income as the case may be). If the courts have ordered visitation rights for the father, you must comply with that order (unless there is evidence that the child is actually in danger from an abusive father).
no
NO!
yes
no
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.
Yes. They are still the child's parent and responsible for supporting their child.
yes