Does Exim support POP and/or IMAP, or do I have to install something else to do that?
Exim provides MTA functionality - that is, it delivers mail. POP and IMAP are two of several ways of reading previously-delivered mail. Exim does not provide that functionality. You need to install POP and/or IMAP daemons; there are several to choose from. The following are links to a few that you can use: