Can the guardian of my child adopt my child??

This situation is obviously more complicated than can be easily handled in a one paragraph question. You should discuss this situation in detail...

Yes.

What would be my child support now?

It depends upon how many children are involved and whether he is above the self support reserve.

I recently had my son emancipated age 20 he moved out and works full time can the mother reapply for support?

She can - but she'll lose.

17 year old custody...

Yes. You would have to file a petition in Family Court.

17 year old custody...

Yes. You would have to file a petition in Family Court.

Would child support be lowered?

Not without more...

Could us ask the Nassau DCSE unit to clear the arrears and close the case (no more future collection)?

It's not clear from your question what the position is - but if you go to court you should go in the county where the order is being enforced.

Typically a support magistrate rules and if you disagree you can appeal to the Family Court.

Can having to pay child support and have no arrears balance cause one to lose employment opportunities?

Apparently, yes.