Is there a document that I can print out for the father of my unborn child to sign his parental rights over?

No. There seems to be a myth that a parent can just sign away their rights. But that is all it is, a myth. There is a sticky note at the top of this forum (I moved your question to Family Law) that goes into this in more detail.

The bottom line is that only a court can terminate parental rights. And courts are very reluctant to do so. So you should be thinking about going to court for child support and custody.

NO, first nothing can be done at all till the child is born.
Next he can not just sign over his rights any way. There are few ways to take his rights away.

Once the child is born, you file for custody and see what little if any visits he wants.