You can blame Microsoft for that. A desktop is the surface area of a desk, to which the Windows desktop is meant to be analogous. In Swedish, that would be skrivbordsyta - literally "writing desk surface". I guess that sounded a bit too contrived, so they used just skrivbord instead.
Understood. But if a user has no context, and only one word appears--then both answers are possibly correct. This is, one imagines, why the system gives two possible answers--because the computer knows that either answer could be correct. In no case, however, would it be logically "incorrect" for a user to use hypothetical abstract reasoning to imagine two situations, one in which it is desk and one in which it is desks.
Sure - but that's near impossible from a computational standpoint to maintain all over the course. While skrivbord is certainly a trivial example, there are sentences which have several hundred accepted solutions. I agree that only being shown one correct solution is annoying, though. Personally, I've resorted to trying out different solutions when I get repeat questions.
Broadly speaking, whenever there's no context, you can enter any single (reasonable) solution.