My vehicle is registered in New York and I would like to know if out-of-state insurance is acceptable for this vehicle?
Unfortunately out-of-state insurance is not acceptable for a vehicle registered in NY.
One other thing, about issuance of a new registration, do i need to surrender the registration if the plates are lost, destroyed, or stolen?
yes. you need to report plates that are lost, stolen or destroyed and surrender the registration in these causes the dmv can issues you a new registration and plates