After updating to Mac OS Catalina, an issue occured where some files could only be deleted via terminal (rm -rf) command, however, dragging the file to the Trash Can, made a trash sound, but the file was not deleted and immediately reappeared on the desktop, also, it could not be overwritten. Files could also not be copied onto the Desktop and trying to save a file had an error message <Cannot save file "Desktop">, even though "Desktop" was a folder and not a file. All permissions were set properly and deleting them via command line was not an issue. Restarting the computer and cleaning temporary files did not get rid of the issue.
The problem was resolved with a "Safe Boot", using the Shift key pressed while starting the Mac. This must have deleted some weird files during the start-up, which created this strange behavior.