Now I see that the material editor always shows the red focused/selected material
from the "Outliner".

However, it would speed up editing quite a bit if there was some possibility
to update the material in the Material Editor when clicking on parts in the Mesh Editor
to the material that is assigned to that specific part.

Maybe only when "edit selected" is checked? Or maybe just another button inside the "Parts" Subwindow to "locate material" of the selected part or something like that?
Maybe just an entry in the right-click window? Something at least to
find a material of a selected mesh-part more quickly.

Let me know what you think.

You can switch to LOD mode F3 key before clicking.
Or if have just one lod then you can also press F4 to disable MESH tab
And F5 Variations tab works.

Ahh, that's perfect!

Thanks.