Just to be clear for non-native English speakers, "Do you have no bread" is not how one would ask this. (Other comments here have good alternative wording.)
And you would also never in Danish ask, Har du intet brød? You would ask, Har du ikke noget brød?
Is "do you have any bread?" correct? From what I understand "har du ikke brød?" Means that I can't find any bread and ask for confirmation, expecting a negative answer but "har du intet brød?" is just asking for bread, right?
I am from Denmark, and actully we would never use "intet" in this kind of sentence. Yours is more correct, har du ikke brød
Although grammatically correct in English, you would never say this. 'Haven't you got any bread?' or 'Don't you have any bread?' would be OK. 'Have you no bread?' would make you sound like you were from the 18th Century!
When do you use intet and when do you use ingen? Is it a gender thing, or plural, or something else?
'ikke' means 'not'. To be able to use 'ikke' in the sentence, "Har du ikke brød?" the English sentence would have to be "Do you not have bread?" or "Don't you have bread?". Because 'intet' means 'no' as in the sentence you're asking about, it is the appropriate word :)