There are things I am wondering about...

Should not cavalry charge always be as equally powerful, when the soldier does carry a spear/lance?

It is depended upon the speed of the horse, when it does run, regardless of that whether it is light cavalry or heavy cavalry?
(the armor does not affect the cavalry charge).

It must of course be used a spear, or a lance, rather than a short weapon like sword.

The length of the lance does determine the reach of the weapon, so that a two-handed lance will hit the enemy sooner,
but is the blow more powerful?

Could not any light cavalry have charged the enemy infantry, then retreated, and repeated it again?
(If the enemy infantry had already depleted all its javelins and would be unable to shoot down the light cavalry).