Do all motions requires a cause?

Yes, all motion has got a cause but there need not be any unbalanced force to cause a motion, for example earth moves round the sun needs no force to make it move. It is because of inertia of motion things in the space move constantly with respect to another.

However, there is a cause for everything and in this universe and the cause exists before the effect this principle is called “the principle of causality” this is the basic law of physics.