Magnetic fields originate from moving charges. Only moving charges feel a force in a magnetic field, not stationary charges. There is no force if the velocity is along the same direction as the magnetic field. These equations also prove that light basically consists of electric and magnetic field. Light is part of electromagnetism.
Average speed describes the speed over some time period.
On a graph of distance versus time, we have found that the speed is the slope. In order to describe speed and direction, we have to be sure of our frame of reference. We describe position, velocity, etc. in a reference frame. Remember the train shooting the ball up. Describe where I am with respect to you.