For the first question, the question intends to ask for the field intensity at a point (outside) near the centre of the plate.
2. Why do you feel that the side near the positive plate should be positively charged? And by the way, since this is a metallic particle, the charge distribution due to induction will not be uniform and the negative charge density will be concentrated in the regions nearer to the positive plate and hence the force will be attractive, i.e., directed towards the plate.