Portia, excellent questions!
I've been puzzling over those questions since I read them... I can only wonder whether it may be possible that in seeing moms/women doing more household chores and dads/men doing fewer chores (therefore thinking in a child-like way that dads/men must be "smarter" to get out of work)... might this carry over to school as a belief that boys are "smarter"... even while girls earn higher grades...?
This seems to fit with the research finding that when a game was described as being for those who are "really, really smart" girls tended to not be interested to play the game... but when the same game was described as being for those who "work hard" girls tended to be interested to play.
Children observing that moms/women do most of the household chores also seems consistent with these children adopting the stereotype that moms/women/girls are "nice".
