So one can never say "har de ingen en hylla"? If 'en' is used, then it has to be 'inte' instead of 'ingen'?
Right. With ingen/inget it's always the indefinite without an article, and in plural inga the indefinite plural. No exceptions to this.
Okay, I'm missing something with these words - what's the difference between "inte"and "ingen"? I swear I use the wrong one more often than the right one.
Inte negates a verb.
Ingen/inget/inga negates a noun.
So is this a grammatical difference between Swedish and English? Like, is the difference that in English you negate the "have" and in Swedish you negate the "hylla"?
In this particular sentence, yes. But both languages can negate either, of course.
Ahh right, tack så mycket!
In the multiple choice version of the question, the correct answer actually translates to 'Do they have no shelf?' - if we're being pernickety... ('ingen' rather than 'har inte en')
Could you also say "Har de inte en hylla?"
According to Arnauti above, yes if you use 'inte en' instead of 'ingen'.