Will a skateboard go faster if you push it with the same force for a longer time?

Yes. The force is measured as "acceleration" and is meters per second per second (or velocity per second) or the first derivative of velocity.

On a frictionless surface in an environment without air resistance, and if the skateboard is a frictionless mechanism, if the skateboard is moving at a constant velocity, that means the acceleration is zero, which means that there is no force being applied to it and it is a body in motion staying in motion.