FAF Client crashes on launch / Startup error

To be sure, remove those folders before you reinstall FAF:

C:\ProgramData\FAForever

%LOCALAPPDATA%\Gas Powered Games\Supreme Commander Forged Alliance\

And double check after the installation that you have the necessary permissions to access and read the files/directory.

Your last log has the same error as your first one:

Caused by: java.nio.file.FileSystemException: C:\ProgramData\FAForever\cache\stylesheets: Die Datei oder das Verzeichnis ist beschädigt und nicht lesbar

(ENG translation: The file or directory is corrupted and not readable)

Hi,
removing the two folders did help.
(Actually the FAF folder wasn't deletable in any way so I just renamed it)

I can now launch FAF normally.
Thank you for your support:)

It is good that the main problem was fixed but it's concerning that you couldn't delete the folder: it's possible that you had some process still running or your disk might be damaged.

Consider a disk checker scan just to know if you need to replace your drive.