I played with the site after some time.

1) I searched drupal.org to find out what we need to find out and what I found is that we should first decide
what we need to find out ;-)
So:

a) we need a way to design our node-type "Open problem"
b) we need a way to attach "categories" (like area) to the nodes
c) we want a way how to search/sort

a) is done by Flexinode and CCK. The latter is supposed to be better, but still somewhat buggy.
(For more details: http://webschuur.com/node/669)

b) is done by (standard) taxonomy vs. (new) category module. The latter seems to be better,
but again, some claim it buggy.

c) for this we should use views -- and this means we cannot use Flexinode in a)

2) What seems to work easily with Category, is creating menu structure for Area (etc.).
I don't know how to do navigation via "pull-down" menus that would be context-sensitive. ;-(

The "only" trouble is that I don't know how to assign Category to nodes ;-(((
May be the taxonomy module is still in the way???