Do you want to register your vehicle in another state?
Yes
If you want to register your vehicle in another state, you must deliver your vehicle registration and license plates to the New York DMV
In case I want to use mail, to where I need to send the documents I file?
You need to send them to the NYS department of motor vehicles financial security bureau PO box 2725 albany NY 12220-0725.
there would be any problem if my insurance company doesn't verify all the information I provide?
Yes, there will be. If that happens, your driver license and/or vehicle registration will be or will remain suspender or revoked.
In case I got suspended or revoked, how do I get a written confirmation of it?
For that, you need to order your driving record or vehicle abstract.
Then what will happens once I provide my proof of insurance?