I did not find an issue for German for the translation of the Spelling & Grammar section.
On the Home tab (in German Start), in the paragraph group, the dropdown for the line spacing options uses Optionen für den Zeilenabstand in Word Online and Zeilenabstandsoptionen in Word 2016 for calling the corresponding options.
On the Insert tab (in German Einfügen) the buttons for inserting images are named differently in Word Online and Word 2016: in Word Online Bild and Onlinebilder, in Word 2016 Bilder (plural) and Onlinegrafiken. My personal preference would be Bilder and Online-Bilder for both apps.
The page layout tab in Word Online is translated to Seitenlayout in Word Online and Layout in Word 2016. I suggest to use Layout for both. The settings for spacing also use different labels on this tab. Davor and Danach in Word Online and Vor and Nach in Word 2016.
The View tab (in German Ansicht) uses Plastischer Reader as translation for the immersive reader. Word 2016 uses Lerntools. However, the features of both differ considerably between Word Online and Word 2016. Awesome features for the immersive reader in Word Online, by the way. I did not found translations issues (German) there. However, the word Plastisch in the ribbon is imho for German not really associative for the features of the learning tools. Unfortunately I don't have a better word, as I find it difficult to find a word describing immersive best.
Step 9 to 12
I could not get the multi-edit mode displayed with the document from the link provided, but I tested it then with between my dummy user and me. I got the following view, where I would like to make a suggestion for a change of the translation of Select someone's name to go where they are editing which would be:
Wählen Sie den Namen einer Person aus, um zu der Stelle zu gelangen, die sie gerade bearbeitet.