Can I renew my car registration in this office?

Yes you can. Also can renew it online is much easy.

How to renew a car registration in DMV?

Yes, you can renew your auto registration here. It's one of the main NYS DMV Office $26 for 1,650 .lbs to $139 for a 6,950 .lbs vehicle. And $140 for 6,951 .lbs and above.

I have a before license nys dmv but I move to ohio staete then I change license into ohio state did I have to report nys dmv that I change my license into different state

Yes