Does a parent who gets off child support and terminates parental rights still have to pay backpay for child support? How can they avoid paying it all?

If you have a possession schedule in the court order that orders you to pay child support, you absolutely have a right to see your daughter as scheduled even during Covid 19. The Supreme Court of Texas made it clear that parents are not to use the pandemic as an excuse to keep the other parent from seeing their children. Unless the mother forgives the arrears, you will have to pay them in Texas. Maybe you read something from some other state, but the Attorney General of Texas is keeping track of the child support you pay and if you get behind, interest will accrue and you have to pay that too.  You are not legally required to buy things for your daughter unless the court order specifically requires that you pay for something in particular like private schoo, day care, specific extra-curricular activities or something like that. In a standard order, you are simply required to pay child support every month. You can enforce your rights to your possession time by filing an enforcement for possession and access.