No objection on my part. Thanks.
@all:
!!!SUCCESS!!!
I finally managed to get it working.
ChickenLipsRfun2eat from ubuntuusers.de lead me in the right direction. He suggested that possibly the displaymanager was getting de-installed.
The procedure was thus:
sudo dpkg --configure -a #unkonfigurierte Pakete bearbeiten
sudo apt-get -f install #Abhängigkeiten auflösen
sudo apt-get clean && sudo apt-get update && sudo apt-get dist-upgrade && sudo apt-get autoremove #Paketcache leeren, System aktualisieren
And after that:
sudo apt install --reinstall sddm
This I think is what got it working again.
When firing up Kubuntu or rebooting I get into the GUI again.
Finally I´d like to thank all of you for your help. I once again learned a lot.
Many greetings and have a nice Sunday.
Rosika 
P.S.:
For anyone interested: the link of the complete discussion (yet in German) is:
https://forum.ubuntuusers.de/topic/kubuntu-bootet-stets-nach-tty1/