Can i filed for child support?

You absolutely are and should. She has a responsibility for the care of her child.

Divorce: Can I enter new evidence of fraud (Ex liquidated and hid assets) after judge said no more evidence may be submitted?

There are conditions under which you can present more evidence. The question is whether the case in at trial, or are you still at the pre-trial...

Will a filed uncontested divorce go through without the notice of continuation of health care coverage signed

That is requirement. You will need to have that done before you can finalize the divorce.

What can I do?

You need to bring this to the attention of the Court with a violation petition.

Custody case

This is strange question with no context so it is impossible to answer.

Can my daughter's father try and sue me if I move her out of the state without talking to him about it?

He absolutely can and probably will. After all, you are making regular time with his daughter almost impossible if you relocate. If you seriously...

Can an ACD get dropped if the original order was dropped afterward or do I have to wait the full year?

Nope you cannot because in a criminal matter it is not your bf against you, but the State of NY.

I have full custody of my daughter and the father is no where to be found, can I change her last name to only mine?

You can, but you need to have the help of an attorney. Either use the Find a Lawyer tab on Avvo or speak to the attorneys who answer this question...

Can I request case be vacated with prejudice

Prejudice never attached in cases like this. You can ask that he be sanctioned in some way.

The DA never prosecutes these cases, however, a good attorney can break down the allegations which would turn the tables for you.