Provided that it doesn't involve payment for arrears, than yes.
No. If you adopted a child and the mother cancelled the adoption, you should owe nothing.
Yes,
no
Yes, he is still the father.
She is entitled to child support regardless of where either of you live. It is your child and you must help support him/ her, and no, she does not have to move back to Nevada.
... eligible to receive food stamps [SNAP] ... yes
yup
send it back
It's likely that one or more States has notified the US State Department of your child support arrearage and, if so, you will not receive a passport. Child support debt is not discharged in bankruptcy.
Generally, no - although there might be an exception for a severely disabled child.
Child support is paid until the child is at least 18 even if the child quit school or graduate early.
Most states do not allow a child to collect back support as an adult. Although the right to child support belongs to the child, support is payable to the custodial parent to assist in the care and upbringing of that child. If the custodial parent did not receive that support, then she (or he) made contributions that should have come from the other parent, and the right to collect the back support belongs to her.