There is a private toll company operating the 407 highway in Canada. They are capable of sending bills to New York drivers. That can't happen without the NY DMV providing vehicle registration data access to a foreign business or an intermediary.

They certainly can under one of the permissible purposes enumerated in the DPPA.

Yes they can. Typically you need a business license or a PI credential. I worked for the DMV.

One example: https://egov.maryland.gov/mva/