Domain hosting, and domain registration are two different things. Dreamhost offers you to host unlimited domains, but you still have to register them - two completely seperate processes (and fees).
Dreamhost pays for 1 domain registration as part of your account plan, and DH will pay for the renewal as long as you maintain the account.
Yes. (the hosting is unlimited, not the registration)
No (if by “monthly fee” you are talkingf about a hosting fee) - you may host unlimited domains in your Dreamhost account without an additional monthly fee “per domain”. If you prepaid for a year, you will only occurr additional fees if you add services, or exceed limit (bandwidth/storage - not likely in either case).
Assuming you are talking about you “hosting plan” being paid a year in advance, and if your “adding a domain” means registering a domain for one year, then the answer is “Yes”. Registration and hosting plans do not necessarily expire/renew at the same time., and don’t even have to be provided by the same company.