Google-apps – Google Apps Calendar without Email

There's an article on this here. I've not checked that it works, but it seems pretty straight forward. The essence is that instead of importing the calendar, you add the URL of your event feed as a public calendar - here's a summary of the steps:

1. In Facebook click on "Events"
2. Click on "Export Events" and copy the URL
3. In Google Calendar go to "Add" under "Other calendars" and choose "Add by URL"
4. Paste the URL you copied from Facebook and click "Add"

[Update: to make answer more complete]
If you run into issues with private events not showing properly then check out eventbusyfix.info. This site acts as an inbetween to clear the private flag and enable Gmail to show them properly (Thanks to prestomation for this tip)
[/Update]

Hope that helps!

The e-mail fetcher would only fetch new e-mails that are on the inbox of the POP account.

IMAP is the the way to go. Here's a quote from another guide:

It was simple: I merely added Gmail as an IMAP account to my Apple Mail client, then just dragged folder-by-folder all the messages important to me onto my Gmail account. It took a while to transfer all the messages (be sure to open the Activity window in Mail to see your progress), but once it was done, all my old messages were safely stored in Gmail and had their original dates! Perfect!