If Gnome and KDE are both installed, the desktop to start can be chosen from the login screen, bottom left. But you need to have both installed.
You cannot set a default desktop, just change desktop as mentioned, next time it will be the same
Looks like your install is not complete. Search for “display-gnome-properties” with all options checked. See if that returns some packages that refer to the search phrase.
BTW. Don’t know it this makes things easier for you, but we have german language subforums…