Yes, you are right in thinking the ball would not move at first, this is why you manually displace the ball to touch one of the plates. I'm not quite sure what the mark scheme is getting at. But if the ball has a neutral charge, it will not move to either of the plates, as the resultant force on it would be zero.
Regards your 3rd point, think about what happens when the -ve charged ball hits the +ve charged plate in terms of electrons. As the ball has an excess of electrons when -ve, when it hits the +ve plate, these electrons flow onto this plate, which leaves the ball with a lack of electrons, therefore it becomes positive. And as like charges repel, the ball is repelled to the negative plate, and this process continues