force exerted by plate on charge =kE where k is the charge of the particle, and E is the electric field at the location of the charge, associated with the plate

For the positively charged plate, this force will be directed away from the plate, and for the negative plate, towards it. So net force on the charge is 2kE, i.e. F= 2kE

If the separation between the plates is doubled, electric field at the center changes. However, since nothing is mentioned, we assume the plates to be infinite, and then electric field is independent of distance, and therefore force remains same.