Hey guys!
I finally found out what the problem is.
It is a stupid one. I tried to produce BSPs everywhere else in my level. And it turned out that I finally could texture my brushes on some points of my level.
The issue is, that you cannot build a BSP while you are in another existing BSP in your level.
What I did early in the beginning of my project, was to set a huge Box-Brush inside my level to define the size of the level.
And now I realized that you can’t build brushes from the inside of this Box-Brush but you can when outside, of course.
I didn’t know that and somehow don’t understand it, but… THE PROBLEM IS FIXED.
(There could be a warning at least to prevent designers from having such situations.)
Sorry guys, all my bad.
I really appreciated all the help and I am very grateful. Thank you!