Are the planets in our solar system in free fall? If I’m correct, the International Space Station is in free fall, but is moving fast enough to keep it’s position. Assuming that is true, does that mean that some/all planets orbiting the Sun are in free fall of the Sun?
Yes. Free fall means the only force acting on a body is gravity. 

The only force acting on the Earth and every other body in orbit is gravity, so all the planets are in free fall.

(There are very small forces from, for example, solar wind but these are minute in comparison to the gravitational forces)