Is there a possibility to show Categories an the subcategories on the same display like in the Attach picture?

Not that I know of. Maybe you can create a 'jDownloads Tree' module for each main category and place them in an article to created something similar.

Hi
As Tazzios said the nearest Scheme is to use several  Tree modules each showing just one Top Level Category in an article.
Think it is a nice display.  If one selects a sub cat does the view style continue?

Have attached a stylised pic of a two column Category viiew that could be a start point.
Colin