Am I responsible for a debt my soon-to-be ex-husband owes his parents?

You should contact a family law attorney in your jurisdiction to determine you responsibility for the debt. It varies by state.

If there is a no contact order due to a pending domestic violence case can the mother drop off kids to father.

I would be very careful having any possible contact. It would be better to contact a family law attorney and have the no contact order revised to...

Am i obligated to let my child spend time with the father if i put him on child support?

In New Jersey, child support and custody are two separate and distinct issues. You should contact an attorney to discuss your options.

Yes. You would have to file a motion in Court and prove to the Court that you are not seeking to avoid paying any creditors.

Will final straining order affect me in Any level ?

A Final Restraining Order can affect your ability to work in some capacities. I am unsure about the effect on your work as electrical engineer. ...