So far we managed to get a basic forum running.
I was without a internet connection for a week and a half, so I couldn't fix some stuff that Garth pointed out.
The main issue seems to be the frame system that the forum uses. But the problem is that I don't know how to integrate the site design into the forum. If I were to somehow include the forum into the main site script URL-s wouldn't work, so I need to find a way for the site script to render the design before the forum being loaded, and yet still have the forum url working properly. Maybe poking with the forum source would help, but I am no PHP expert...
Besides that what else could be done, note that we are limited to PhpBB functionality, and I can't mod the source too much to add custom features.