Question

Is there any point on the trajectory where v⃗ and a⃗ are parallel to each other? if so, where?

Answer 1

In a projectile motion, there are two components: horizontal and vertical. The vertical component is in a uniformly accelerated motion. The motion is always directed downwards due to the force of gravity. The horizontal component (constant velocity) on the other hand must move in the horizontal axis. They can never be parallel on the trajectory. 

They can only by parallel during a free fall motion, wherein no change of horizontal direction occurs.