No. If a person terminates his/her parental rights they are severing all maternal ties, rights and responsibilities to that child. It will be as if the child never existed. Neither parent nor child will benefit from nor be an heir to the others estate.
This depends on the court order. If you only get your parental rights terminated, you may still be obliged to pay child support, but the court order might also cancel the legal obligations that follow parenthood.
Parental rights can only be terminated if there is someone willing to fulfill the role as parent. At which time you have no legal obligations including child support.
No clear answers. Often rights are not terminated until there is a reason for such termination such as a new marriage. In that case the new parent often adopts the child in conjunction with such termination and the new parent takes on support of child.
Once parental rights are terminated there is no longer any financial or legal obligation to a child. This includes child support, visitation, inheritance and other rights. However, family law rules and regulations do differ from state to state. Always consult an attorney for legal advice.
You do not pay child support when you terminate parental rights. You are basically giving
away all legal rights of custoday to that child, including responsibility.