Not possible if you don't have one.
no
NO!
Generally, no.
yes
no
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.
Yes. They are still the child's parent and responsible for supporting their child.