Can the father of my kids sign his rights over completely without someone adopting them?

Such a thing is impossible in NYS. There needs to be an adoption or a termination of parental rights.

My divorce decree shows I had to start to refiance a year after we got divorced which I got denied can he force me out of house

You need to document you attempts to refinance so that in case a case is brought, you will have a valid explanation.

How do I get the courts to intervene?

It sounds like you need to enforce your current order. She is in contempt for her violation of that order. Hire an attorney and move ahead.

Was I lied to?

What is your question? It is very unclear.

There is no statute of limitation regarding these sorts of things. Speak to your attorney.

Refinance? Husband left. I don't have an address he has been gone 9 months. We have a home with both our names on it.

Seek the aid of an attorney. You will not be able to refinance as you will need his signature to do so. An attorney can help you by either finding...

Is it likely NCP will win downward modification?

The best thing you can do for yourself is hire an attorney to help you with this matter.

I have a rental property which is currently being rented by a husband, wife & their 3 children.

Speak to landlord/tenant attorney as soon as possible. This is not a Family Law question.

When should habeas be filled?

This is a criminal law/immigration question, not a DV question. Repost this in the appropriate forum.

Your grandmother does not have standing to seek a paternity test, however, ACS does and can. Speak to the social worker.