If a father signs his rights away does he still have to pay backsupport and current childsupport still in Arizona..

Where do you get the idea you can sign away rights to a child? A child is not a car.

A father can not just sign his rights away, that is a myth, he can not ask for cusody, not ask for child support.

If the other parent is going to remarry and has a new husband to adopt, then he can sign over rights for that.

You might want to check out this sticky:
https://www.askmehelpdesk.com/family...st-116098.html

It's a good idea on a site like this, to browse around before posting. You can often find your question already answered.

As noted, there is a myth that a parent can just sign their right away. Its only a myth. Only a court can terminate rights and they will not terminate rights to let a parent out of paying support.