The official translation given is "I do not have apples." I don't know where the "any" came from, either. But in actual conversation, away from formal lessons, the "any" might be used as an intensifier, to emphasize that no, I'm not just saying that I have no apples to spare, but rather, I don't have any apples at all, not even one, not even what I'm holding on to for myself.
I guess that when there is NO object, then it is singular ( I have no apple)
In the following sentences, apple/apples is the object of the verb, so I'm not sure what you mean. Perhaps you meant article, such as "an/an" or "the"? You can still determine whether it's singular or plural by the form of the noun. "Mela" is apple, singular and "mele" is apples, plural.
I have an apple / Ho una mela.
I have the apple / Ho la mela.
I don't have an apple Non ho una mela.
I don't have the apple Non ho la mela.
I have the apples / Ho le mele.
I don't have the apples / Non ho le mele.
I have apples / Ho mele.
it's false we can say sono fartalle so doesn't have any relation with it
Why is it wrong to translate like "I don't own apples" since "ho" means either have or own?
Is it always like this? 'non' always comes first before anything like 'ho' or 'ha'?