POP and IMAP are separate protocols. You wouldn't set up a mail server with IMAP so your clients can use POP, you would set it up with POP.
As to the second question, the domain name doesn't need to be there because your DNS service is working properly. If that goes down, nothing works!! There wouldn't be any conflict caused by another mail server on the network so far as I know. It's just gonna be acting as a MTA at that point, and it acts pretty much like anything else when it looks for another machine on the network. No worries AFAIK.