It seems natural and appropriate for an older man to call a non-relative boy/young man “son” to convey endearment. Although I’m not sure, I think it’s unofficially reserved for men’s use only (the older person is male).
However, if he younger person was female, “daughter” seems awkward.
Is there a analogous term of endearment for young females? If so, it is reserved for older women’s use? Or is “daughter” used?
"Lass" or "Lassie" are commonly used in dialects in the north of England and Scotland to address girls and young women in a friendly way, although they are sometimes considered sexist so I'd be wary of using them. (Daily Telegraph)
I don't think there's a term of endearment or form of address common across all English-speaking regions, but terms of endearment still tend to be quite local or region-specific.