All parental rights? That depends on state law where you live (or country if outside of the US). Some states have no provision for voluntary termination of parental rights and in most cases, those that do only allow it in preparation for adoption (sole physical and legal custody by one parent doesn't count). And even if you can terminate your parental rights, that will not terminate your obligation to pay child support. All it will do is terminate your right to see your child and have any say-so in their life.
That depends on whether the non custodial parent has any legal custodial rights and whether those rights are sole or joint. If the non-custodial has sole legal custody, probably. If not, then no, not for a minor child, not without the permission of the parent with sole or joint legal custody. There are different types of custody, physical and legal. Check your custody order before you proceed to get an answer, or contact an attorney.
You would have to call the court house for legal papers on terminating parental rights.
"custodial" ... "their" ... In general, parental rights are terminated either preparatory to an adoption, or after a trial in which it is determined that the parent is unfit. In any case, termination of parental rights does not, in itself, terminate child support.
No. Only the court can enter an order of temporary custody. With the non-custodial parent incarcerated and with the consent of the custodial parent the court would likely approve a temporary guardianship that is in the best interest of the child.
if a non custodial parent reuses to sign a passport the only option is court. A judge can decide if it is in the best interests of the child to leave the country.
No, but that's not possible unless approved by both the other parent AND the court, provided the other parent is not now, nor in the future, collect Welfare.
Don't think so. The key word here is "custodial".
There is a lot missing, such as was the custodial denying access? Also, did the custodial sign the Visa Application for the child?
No
You must go to the family court to see about getting the custody changed.
Yes, voluntarily relinquishing your parental rights does not excuse you from having to pay child support.
It has to be done before, and approved by the court, but the primary must not now, nor in the future, be on Welfare.