My son is 14 years old and I have not been involved in his life for several years. I am currently paying child support and owe the state and mother back support. His mother has just got married... so my son has support and I would like to pay her the back support I owe and the state, but no more than that... would termination of my parental rights make this possible ?

No, not really. You could well still be responsible for child support. Please review the other threads on this very same question:

https://www.askmehelpdesk.com/search.php?searchid=1059287

No, but if the mother agrees, you can make it to wear you don't have to pay anything more than that.

If the new spouse would like to adopt the child, then you can stop paying current child support,

But no, you can give up any right you want, but your rights is not your obligation of child support, that can not be given up, if it could there would not be people in jail tonight for not paying it.

So you will pay child support no matter if she got re-married, that has nothing to do with it at all.

Not true, if the child's mother doesn't press you to pay and doesn't have it court ordered, then obviously, you won't have to.