Ten years ago i purchased car iinsurance than i moved. they changed mailing address but not the area for insurance coverage.

I would give the company the opportunity to resolve the issue. Then if you are not satisfied contact the NJ Department of Insurance.

Am I responsible for rent if the person who signed a new lease for my unit failed to actually move in?

I disagree with with counsel. If the LL notifies you it is not going to hold you liable and then the new tenant defaults, you are off the hook. ...

Do i have a case

File a motion to vacate the prio decision based on newly discovered evidence.

I'd have to agree with counsel.

Must i pay my landlord if he does not have a certificate of occupancy

Yes, but if the unit is illegal the LL is subject to a penalty the equivalent to 6 months remy

What law permits landlords (new/old) to move a tenant from one floor to another against their will?

Assuming this is a good faith manouver, LL has the right to do it.

Bail bonds put a lien on my house till I paid them off but I paid in full and they have not taking it off.

If you paid in full they have to release the lien. You should retain counsel to help with obtaining the release

What are the options after being served a writ of execution for our personal property.

If anything is seized, you are entitled to a hearing. You can raise these issues there

My sibling claimed the total proceeds from a life insurance policy on our parent.

You need to get the policy and see who the beneficiaries are. Assuming that you are correct, be prepared to sue the Insurance Co and your sibling

Is landlord able to charge for rent after someone dies in NJ?

Without reading the lease, generally speaking, the estate would be liable. You may be able to negotiate a deal with the LL. Thats where I suggest...