Ok, I take a shot. It has been a while since I dealt with the stuff, and I don't live in the text books, so....
A PDC and a BDC a primarily the same, both manage security and resources in the domain, with the exception that BDC is the backup. A BDC only becomes active when it is promoted to a PDC status. Also the PDC usually is the "master browser" for the domain, keeping track of the netbios stuff.
To answer the first question: A BDC is the same, but non-active. It receives the same updates from the domain, put on a replicated cycle. (don't ask me what that timing is, I can't remember the text book answer. If I had to guess, it is something like every 15 minutes).
Answer for the Second Question: If the BDC isn't promoted and the PDC is offline, Some user may not be able to login to some network resources. Based on cached profiles, etc, some users may "look" like they logged into the windows desktop, but not really (it may give them something like 'domain controller not found'). Anyone using that domain to authenticate to a network share, folder or website, will probably be denied access without much of an explanational error message.
Tekinfarmland