They were in the club

I always assumed it was the "you were left at our doorstep as a baby" kind of story.

She grew up in isolation, so they wouldn't have had to tell her anything. Aurora never would have known what a parent was unless the fairies told her.
Unless she noticed that the forest animals always had a male and female parent, but considering she couldn't actually talk to them and it's not always noticeable who an animal's parents are, this may not have occurred to her.

Not sure. I think they never really say anything about her parents even after she was told that she's the princess.