(1) In the admin console you can set the MailPollingInterval for accounts, or allow them to set their own (this is disabled by default)
(3) Yes, otherwise what is the point of a filter?
you might see some odd things though. For example I seem to have to use From->contains to filter by email address, rather then From->Matches Exactly.
(4) I think that might be a bug that the external accounts don't show up. Of course it could just be the limited functionality of the lite client. You could try searching
Bugzilla Main Page - Zimbra and entering a bug if you don't find anything. As far as external mail... refresh has always worked for me, but see (1) for something that might be related to this.
(5) I prefer IMAP as it syncs with the server, rather then downloading the messages. Also IMAP is a much more modern protocol. But in the end it doesn't really matter, POP3 has been hacked up enough to provide enough of IMAP's functionality for basic email access.