Why is "Barlangokban sötét van" wrong?
Because the definite article is missing. It needs to be there. Hungarian has its own rules that are not the same as those of English.
Why is it "van" and not "vannak". The noun is plural.
The noun 'caves' is not the subject of the sentences. Th (implied) subject is 'it', which is singular. Similar in both English and Hungarian.