My ex-spouse wants me to sign a document giving financial advantage and they wont per-sue charges, is that considered blackmail?

It could be. It depends on the wording and the specific situation.

It will go a long way towards solidifying your ability to move states.

I have life time alimony he stopped paying around six years ago can go after him to get it he now lives in ct?

Yes you can. File an enforcement petition.

Father of unborn child does not want child. Can mother put his name on birth certificate without his permission & signature?

No. He would need to sign the acknowledgment of paternity. Once the child is born you can sue for paternity.

Child support?

Do you have sole legal custody? Also it depends on his finances.

My son is 16 and has been living with me for the past 7 years he wants his mother to start paying child support.

You can file for support. The support would be paid to you not the child.

I filed a divorce 5 years ago where I did not mention the kids on the divorce because I did not know where the father was at the

It is a problem. You need to discuss the situation with a lawyer more details are needed for any advice on how to proceed.

Can you have a separate savings account after your married that would not be considered marital assets ?

You can but then you cannot commingle marital earnings in that account during the marriage. It is safer to have a prenup.

How can i get my Family Court Records?

Go to court with your if and ask for the records room. They will give you a copy of the order.

In New York State, can a custodial parent move with the child to another county without the non-custodial parent's consent?

The grandmother would still need court permission to move to another country with the child.