Pavane:
As to who is singing to Danny, I would go for the option of a lover. This Thread discusses the singer, and there I have added the alternate lyrics provided by the author (Fred Weatherly) to be used when sung by a man.
The fact that he intended 'Danny Boy' to be sung by a woman, or 'Eily Dear' to be sung by a man seems to make it clear that it is neither parental, nor filial love he was writing about.

CHEERS
Nigel