Does בן זוג mean a partner in the romantic sense, as בת זוג does? If so, is there any reason why "boyfriend" shouldn't be accepted?
Yes, it means romantic partner, wouldn't do for a business partner etc.. I'm guessing boyfriend is not accepted because בן זוג implies a stronger commitment than boyfriend, for that we typically use the word חבר which is ambiguous and causes confusion and embarrassment no end. Fun! :-)
Oh, I can see how חבר could be wonderfully anbiguous. I only asked, because בת זוג was translated as "girlfriend," of course.
Sure it does; there are many reasons half of a couple might not work. He could be temporarily unemployed, or disabled, or he could choose to stay at home to take care of children (although that's also a kind of work, albeit unpaid).
A lot of the sentences on Duolingo make no sense. Remember "I am a mushroom"? Total giberish.
I would suggest that Duolingo is intended to be for all. If you cannot stand to use a program that is also being used by those different from you, though, it may not be for you.