As a projectile falls vertically, it also travels horizontally. Is the distance which it falls vertically effected by its horizontal velocity?

no

its kinematics

the acceleration due to gravity and the initial vertical velocity are the only thing that affects vertical distance

the answer is yes

it has kinetic energy

reason

an object has kinetic energy when you stop the force carrying it, the object will stay in motion.

hope this contact me for more questions if you'd like: )