If you'll provide a link to the rule, I can try to give you an answer.
You can get arrested in all US states if you don't follow the court order to pay child support.
you have to pay child support as long as your child is under 18 years of age
Yes, both have to pay the state.
No but past due child support may still be owed
Yes, the right of a parent to be in his or her child's life has nothing to with whether or not he or she is paying child support. The court sees them as two entirely different issues.
if a court order exist.
Yes; however, if the chid is receiving SSA based on your earnings, that counts as chid support paid.
yes it is mandatory only if you have the father on the birth certificate
http://www.ocffr.org/
Child support in Ohio usually continues until the child is 18, and up to the age of 21 if the child is in school. Whether or not you have to pay child support if the child is living with the noncustodial parent depends on the support order that it is in place Typically you can expect that you will have to expect to pay support.
see link
This sounds like a hearing held in Ohio to determine whether the child support payments of a non-custodial parent will be changed (adjusted).