Aren't always sounds awkward when expanded from the contraction, as does "isn't".
Isn't there anything else you want? (sounds good)
Is there not anything else you want? (sounds weird / overly formal)
Your example is bad. Aren't there any oranges is perfectly natural.
To me that would be more like ¿Hay naranjas?. By putting the no here it makes it a different type of question. This way it's like the person asking the question assumes the answer is yes but is confirming. Like, "Aren't there any oranges, I just went shopping yesterday". I think what we're learning with this example is that by putting the no in front we can ask questions like we do in English. like the difference with "¿Tienes que ir a la escuela hoy?->Do you have to go to school today?" just kind of a straight up question vs. ¿"No tienes que ir a la escuela hoy?->Don't you have to go to school today??". The second version means I do know you have to go to school, I'm just wondering why you're still in bed.
Aren't there oranges? is what I would definitely say... and I'm pretty sure it's what everyone I know would say... I understand that it should be accepted with the "any" included, but it should also be accepted without. I'm really confused about why they think that all native English speakers would use "any" here... It should be accepted either way.
I have no idea what you're trying to express with that. If you give us the complete sentence you've tried, we can certainly help you more.
But I can tell you one thing: the apostrophe has to go in a different place: "aren't". You're throwing out the 'o' in "are not", and the apostrophe has to replace that 'o'.
These sentences are completely without context, so I'm not sure why so many people can say what most English speakers would say. Let's say my wife sees me grabbing a bag of potato chips. She says, "Put those chips down, aren't there any oranges over there?". Also we could be at the store and I go walk over with a couple of grapefruit. "Why are you bringing those grapefruits, aren't there any oranges?" As a standalone sentence, yes this is awkward, but just take it for what it's trying to teach you, which is to use "no hay..." in similar cases where we would say "isn't/aren't there..."
If your kid is complaining about being hungry you could say "¿Hay comida en la nevera?" which to me seems like you really don't know the answer or you could say "¿No hay comida en la nevera?". Where you're like isn't there food in the fridge?? why are you sitting here complaining.