My problems are solved - not the way I originally planned though :-)
The reason why I wanted Zimbra was its ability to share agendas. The rest was merely an extra.
I've tried reinstalling following the instructions given above and on Aiman's site. Halfway I took a break and decided to give another method one more chance: publishing Outlook agendas on WebDAV (hosted by XAMP on Windows 2000), which I never got to work.
Luck must have been on my side today, as I did manage to get it working within 5 minutes.
Now Zimbra might be able to do the same thing even better, but I'm satisfied with the current solution. It's all I need really.
I'm just mentioning this so that people won't spend too much time on my problems. You've all been very helpful. If you really want to get to the bottom of this anyway, I suggest you try installing Zimbra on VMWare + openSUSE 10.2 to see if that works.
Thank you for all your help.