There is not much in her life that she can control right now so this is a way for her to gain some control over a part of her daily life. I wouldn't worry but if it has you concerned you should make an appointment with a therapist. I think it is simply an issue that she wants some things that she feels are under her 'control' and is completely normal at this age. All kids at 3 do not ever sit still.
She may. But it is not really a bad thing if you foster it the right way. You may want to speak to your pediatrician. My 10 year old has it as well as I, but it was not an issue for him until 2nd grade, then we had trouble with him and homework b/c he had to have all his letters the same size on the paper and numbers lined up, he would erase until he ripped the page. We finally had to have him put on medication.