No, he doesn't.
That depends on state law where you live. It can vary.
No, but he can't.see link
Only if he owes back child support. This can be written in the agreement that all arrears be terminated and his rights will be to the child if he signs.
No, but he can't. see link
No, but since he can't, it doesn't matter. see links
in the state of Georgia can unwed father give up there rights
last i knew unless there is a step father willing to adopt the courts will not let you give up rights if there is a step father willing to adopt you will not have to pay child support
Yes as they are separate issues and are addressed separately. see links below