Answer
No. No. No.
Work Step by Step
The force that a charge feels in an electric field is $\vec{F}=q\vec{E}$. The proton and electron have charges of the same magnitude but opposite sign, so they will feel the same magnitude of force, but in opposite directions. Force is a vector, with magnitude and direction, so these forces are not the same.
An object’s acceleration is the net force on it, divided by its mass. Since the forces on each have the same magnitude, but the electron’s mass is much smaller, the acceleration of the electron is much greater in magnitude.
They will accelerate in opposite directions because their charges are opposite.
