After 2yrs. Does the father has to payback child support even though the mother knew the fathers workplace and she never revealed the child to him.

The father has to pay child support according to the court order. Where or even if he works, the mother knowing or not knowing things. It all depends on the court order.

Does the mother have a court order for child support from the court ? If yes, then the father has to pay.

Next you can not just give up rights to a child,unless the other parent has a partner wanting to adopt. That has been asked and answered at least 1000 times on here.

ANY question on law needs to include your general locale as laws vary by area.

Most areas do not allow retroactive support prior to filing. But there are exceptions.