Indeed. Check this out, I just found this article on gelato. It has both English and Italian translations too (and the gelato in the pic looks scrumptious!)
Not exactly Italian-related, but in Portuguese we have the same problem with specific things. You could absolutely refer to a tomato soup (singular) or a soup of tomatoes (plural), and people would still understand you. Perhaps not exactly in what the rules say, but how the language is used. Maybe that's what's going on in Italian: a soup in the style of tomato, but an ice cream with the flavour of apples.
Well, I'm not sure if this is what you are asking, but 'le' is only a definite article, feminine, plural form, and 'alle' is a combination of the preposition 'a' with that same article. (alle = a + le). So, anywhere you would need to use that preposition 'a' with the feminine noun in plural that requires the article 'le' you would need to precede it with that 'alle' combination.
The Italian preposition a can mean "to," "at," or "in," depending on how you use it in context. You use it in the following cases:
When saying that you are going or staying somewhere, as in 'Vado a Milano.' or 'Si trova a Venezia. (It can be found in Venice.)
Before indirect objects: 'Scriva a Rita.' or 'Scriviamo alle zie. (We write to our aunt.)
In combination with certain verbs: andare a... (to go to) (Vado a casa VS Vado alle piazze.) fermarsi a... (to stop) incoraggiare a... (to encourage) invitare a... (to invite to) insegnare a... (to teach) riuscire a... (to succeed) venire a... (to come to)
In the following phrases: a mezzogiorno (at noontime) alle tre (at three) barca a vela (sailboat) sedia a rotelle (wheelchair)
Attributive nouns are usually singular: http://www.englishspark.com/en/blog/stumpers/447-noun-modifier-attributive-noun
I agree that "the apple ice cream" is incorrect unless the situation is that you knew that in the past they have had that flavour and you are referring to this particular one. However, I (a native English speaker) answered "do you have an apple ice cream?" which was also (and in my opinion, mistakenly) judged incorrect.
Because the word apple functions/serves as an adjective here, and adjectives are hardly ever (almost never) in plural. That's why we say 'a three-year-old boy' and NOT 'a three-yearS-old boy'. There are some exceptions though, which you can find at http://david-crystal.blogspot.com/2010/05/on-plural-adjectives.html
I think "Have you apple ice cream " is incorrect english. I think it should be "Do you have apple ice cream? " or " Have you got apple ice cream? ". If you substitute the verb " have " with any other verb e.g. " eat or buy or sell " you can see the problem. You cannot say " eat you apple ice cream? " or "Buy you apple ice cream? " You must say " do you eat " or " do you buy apple ice cream? "