What supporting evidence should i send

You should repost your question under the immigration practice area rather than family law.

Is there any difference in how married fathers (separated) are treated in family court versus supreme court in New York?

It does not sound like either of you want a divorce so the Supreme Court is not really an option in your case. If you want to attempt to get...

Move away, NY to CA

What is your objection to your wife relocating if you do not reside in New York?

Executive Law § 259-i[3][c] requires that a parole board must afford a preliminary revocation hearing before a hearing officer within fifteen days...

I suggest you review CPL 170.56 at: http://codes.findlaw.com/ny/criminal-procedure-law/cpl-sect-170-56.html

Can I request to relocate in the middle of a custody battles

I suggest you read the decision in Tropes v. Tropea at: http://www.courts.state.ny.us/reporter/archives/tropea.htm

My ex husband is getting married and is planning on moving to California,?

Any parent at anytime can attempt to obtain sole phyiscal and legal custody of their child by simply filing a petition in family court. But, then...

Am I violating court order if my son refers to my husband as step-dad?

I do not think your son identifying his step father as his step father to third parties would be considered a violation.

What are the disciplinary actions taking on a minor (15 years old ) be if he was charged with a c class felony ?

Is the case being handled in Family Court? If so see: https://www.nycourts.gov/courts/7jd/courts/family/case_types/juvenile_delinquency.shtml

You are being offered to plead to a three point speed.