Ok I found an easy work-around for integrating my page into PunBB.
My layout looks like this:
--------------------------------------------------
| header (PunBB) |
--------------------------------------------------
| ------------------------------ |
| left | forum (PunBB) | right |
| | or custom content | |
| ------------------------------ |
| ------------------------------ |
| | footer (PunBB) | |
| ------------------------------ |
--------------------------------------------------
| footer |
--------------------------------------------------
Problem was that the custom left menu and the resulting custom content by clicking on the menu only reacted
to my custom styles if it wasn't already declared in PunBB or if I put an !important next to it.
The solution is to take out the class="pun" from the template and only wrap it around PunBB content, in this case
the header and middle part.
Problem 1) from the first post remains though