The E-field vector always points in the direction of the force experienced by a positive test charge, placed at that point in the field.
Case (a) the negatively charged particle will accelerate to the left, thus increasing its speed and its kinetic energy.
Case (b) the positively charged particle will accelerate to the right. Initially, its speed and kinetic energy will decrease.
However, if the force continues to be applied to the right, it could slow down and stop, and its speed and kinetic energy could increase again, to the right.
The last part of the question - in both cases, work is done by the electric field on the particle (that is how the HSC Physics course explains the interaction).