I quit my job and requested child support modification, the judge refused to lower the amount.

You did not get ripped off. It appears that the court ruled properly.

Will the case be dismissed, or will it be decided on the merits of the case? And if so, what is the point of a traverse hearing?

I'm assuming that there was a default entered against you? The court will likely vacate that default. The other side will likely then commence...

I would like to know which type of lawyer I would need to appoint concerning a petition?

Elder law.

Generally 2 years in Family Court.

Can I get custody/visitation if I owe support?

You can file for custody or visitation. Arrears should not cause the court to refuse to provide you with visitation.

In divorce process 3 years, child support & custody are not ordered but child lives with Mom, Dad is keeping child hostage ,HELP

Have you made a motion for temporary custody, child support and maintenance? That's the first step.

In New York State can my wife's divorce lawyer be the magistrate in a child support hearing

Ask the magistrate to recuse himself / herself.

My sister is threatning to take her son, that my grandmother raised, BC my sister is a drug addict. My grandma has temp custody

A notarized statement is not the same as a custody order. I doubt that the police would enforce custody based on it. The best option (as you...

I filed Separation papers with Nassau County over 10 yrs ago, what is the next step to file for uncontested divorce

File a Summons with Notice and have it served on your spouse.

Can a women be on public assistance and lie! Saying her baby's father is no where to be found? But he lives with her?

Unfortunately these things happen all the time. You can report the fraud but, in all likelihood, nothing will come of it.