So - hours later I've installed Zimbra again and I've got a DNS server running (powerDNS).
It seems to work so far.
I read something about a zimbra Admin UI, /zimbraAdmin should be the URL I guess, but I don't know how to access it.. I either get a 404 on port 7780 or request not allowed on port 80.
UPDATE: Got it,
https://localhost:7071/zimbraAdmin/ is the correct URL I guess.
But all I get is an empty page right now.. I'll check the logs.
UPDATE: I've hit a bug. I know, Konqueror is not a supported browser. zimbra told me that when I tried to access the user interface. But it just throws a NullPointerException while trying to parse my Useragent String.
Works just fine with Firefox.