1.you never see Queen Hyrule and links mother was killed in the war.
5.There's also Zelda's lullaby. Impa clearly says she only teaches it to "members of the royal family" and then immediately proceeds to teach it to Link.
It's important here to note that Impa herself isn't a member of the Royal Family, she's just Zelda's attendant, and yet she knows the song. The song is used to prove Link's connection to the Royal Family when he's in Goron City and to be permitted entry to Zora's Domain. This means both Darunia and the Zora's know the song (otherwise how would they recognise it?). Darunia is not a member of the Royal Family (he mentions the King of Hyrule is his 'Sworn Brother' but he also gives this title to Link which shows it is just an honoury thing, displaying a close relationship between the two. It's similar to being named 'Blood Kin' by the Orcs in Skyrim) and none of the Zoras are members of the Royal Family either (in fact, they have their own Royal Family).
When Impa says "Only Royal Family members are allowed to learn this song," it's fairly clear that this is not a strict, literal rule and doesn't mean Link is an actual member of the Family.
As for never seeing the Queen, well, we never see the King either. What exactly is your point there?
Just because we know Link's mother died during the war doesn't in anyway mean his mother was the Queen. Several people have pointed out that the Queen would have more safety staying with her husband, the King, than fleeing to the woods and even if she did, why would she take only one of her babies?