Technically the child is not being supported by the custodial parent. Check your state laws.
no you just sit out your sentence, then you have to pay back what you couldn't pay while you was locked up.
I wouldn't think so, if your child is under 18.
I suggest you ask the venue that issued the order to suspend payments. However, you owe any unpaid support that accrues until that happens.
This would be up to a judge. see link