I have a question, When the father gives up all parental rights to the mother, Is he still obligated to pay childsupport?

Not an expert, this is just an opinion. Your child is not going to stop needing things. This is his financial responsibility, and for you and your child's sake I hope so. Every that does this does not deserve the title "father", "dad" hope you get the help you need this is a tough situation for yourself and your child...

Yes, he will still be obligated to pay child support. If he weren't, don't you think there would be a line a mile long at the local courthouses of the men and/or women trying to get out of support.

All giving up your rights means is that he is no longer able to make decisions regarding the health and welfare of the child. It does not mean that he is still not financially obligated to pay for the child he created.