Your question is unclear, but if you want to use you NY notary to notarize documents in NJ until you get NJ - the answer to that specific question...

Remedy for misconduct/ violations?

Not really an immediate remedy. You can file a complaint with the grievance committee but I will admit those usually go nowhere.

Most common situations would be family offenses.

Yes, I assume you have a temporary order from a family court or criminal court. Those orders do not restrict travel.

You need an attorney because AUO is a misdemeanor punishable by up to 364 days in jail.

Unless you suffered a serious physical injury, there's nothing else you can do. Collect your check for the damages and move on.

Last months rent means you don’t pay rent for the last month of the lease term. So you’d essentially wouldn’t have to have anything returned. If...

Notice is not legal. You are entitled to 90 days notice. A 30 day notice is defective. You hold so much leverage in this spot you could probably...

How can a person in Upstate New York be charged with a crime of Arson if there is no proof he did the crime?

A confession is convincing proof of a crime being committed.

I have court order of protection serving papers

Have you asked the court clerk? Usually they take care of this. Most of the time it’s the sheriff or local police that serve these documents.