The answer that was given, "Does he have his insurances?" is not the way a native speaker of US English would say it. Instead, it would be "Does he have his insurance policies?" If it only refers to one kind of policy, it would usually be "Does he have insurance?" not "his insurance."
I put "Does he have insurance?" and was marked wrong for omitting "his" before the word insurance. Can someone tell me does this sentence mean to question whether or not the subject has insurance, or is it meant to question whether or not the subject has someone else's insurance?
Case and/or gender determine the endings...
The current official translation is stupid, but yours seems to be a bit too free for my taste. In German as well it's perfectly fine to say "Ist er versichert?" I can't see a motivation for switching between these two ways of putting it just because we are translating.
The German sentence is a bit weird and seems to make sense only in a special context that we are not given. The closest translation that would fit in most such appropriate contexts is probably one of these: "Does he have his insurance?" "Does he have his insurance policies?"
Surely "has he got" = "does he have" (even when I use the stupid word 'insurances')
I agree with all the commentsmade about about the word "insurances" - which I have never heard used in English. I see these comments were made years ago - so Duo's system doesn't respond fast!