The fact that you got this log line,
[warning/api/econnrefused][localhost/v3/page/html/Main_Page/3] Failed API request, {"error":{"code":"ECONNREFUSED","errno":"ECONNREFUSED","syscall":"connect"},"retries-remaining":0}
means that your VE is probably setup correctly. It is at least communicating with Parsoid.
ECONNREFUSED is problematic though. It means that Parsoid can't connect to http://192.168.0.102/wiki/w/api.php
I have setup the whole topology inside of a virtual machine. The main problem was that the outbound packages from the VM didn't go over the iptables rules which I had set only for the PREROUTING chain. So I had to add an OUTPUT chain for that. And now everything works fine.
Thanks to Arlo Breault for helping me to find and solve that problem.
Best regards Julian Loferer