How many:- and who:- other than the two main sides to the Car Insurance contract...the broker or insurance company and me:- are involved? Is there just usually an extra one? A finance company and no others?
An insurer and underwriter are the same thing. The contract is between the insured and the insurer. There aren't any other partners. Brokers have a separate relationship with the client, finance companies can be named as interested parties, (like mortgage lender on house insurance), but aren't part of the contract per se.