Can I move out of the the state if I have sole legal and physical custody of my child and the father has no visitation rights?

To be on the safe side, I think you need the permission of the Court. However based upon your facts, if you do not get that permission and proceed...

How would I go about calling someone, in as a witness to my case.

This is why people needs attorneys. These are the sorts of details you need to know in order to litigate a case. You can just call the person....

Can i get domestic partnership even though my divorce is not final

Your divorce needs to be finalized.

How Likely is it for the judge to deny the DAs decision

It is very rare for a judge to not agree to the deal struck by a DA.

When my ex pays alimony & child support, but does not pay anything else, including children's medical, daycare, school program

The only answer to this question is that you either need an attorney or should be speaking to your attorney. You need to speak to an attorney in...

Child custody

This is a matter for which you need an attorney.

Why

WIthout seeing the document, no one can tell you what it means.

Can i get another lawyer, if the lawyer hasnt done anything in 4 yrs?

You can always get a new attorney.

How do I transfer the house into my name only (have my husband's name taken off) prior to finalizing the divorce?

Please see my answer to your exact same question.

This is something your attorney should be advising you on and if you do not have one, you need one immediately.