I think Palin meant to say "the Crown," i.e. the government of the day (the politicians supported by a plurality of the Commons) that exercises the royal prerogative.
Nah, she is pretty clueless. And don't forget, this story came from the time when she had only just been plucked from Alaskan obscurity and became expected to know how things actually are in the world.
Plus, she's just not the brightest bulb.
But your undying faith in her is quite charming. Maybe you could ask her to the prom one day?
Do you mean that JJ sees starbursts every time sister Sarah flashes her smile on TV?