Suppose electrons enter a uniform electric field midway between two plates at an angle ¦È0 to the horizontal, as shown in the figure

Answer 1

I have no idea what your figure looks like but in general this is a projectile problem
You have a constant velocity normal to the E vector (which is constant between the plates) like horizontal speed in a projectile problem
You have a F = q E problem in the direction of the E field just like m g in your projectile motion problem

the result of course is a parabolic path.