Thanks for your help!!! Problem seems to be solved. “seems to be” because I cannot yet test a few keys, which only work while writing Japanese.
I am using KDE, but the 3 examples you explained in details made me looking again into
System settings > Input devices > Keyboard > tab: layout
The trick is to check “configure layout” (until now I hesitated to check the field to not mess up things more).
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The keyboard layout image for the Japanese (ODAG 109A) does not exactly match the keyboard layout of my Japanese version of Thinkpad x240. However, if there is interest I am willing provide a picture and the Japanese characters printed on some keys. Please advice.