E=mc^2 energy = mass * the speed of light ^2 is mass moving at the speed of light ^2 in this equation? And what would Volume vc^2 be...Mass?

The m in E = mc^2 is the object's "rest" mass. The mass it would have when measured in a frame of reference where it is at rest.

The equation doesn't prove that volume can't move without mass. It's completely silent on this issue.

The equation doesn't mention volume at all, and your speculations about volume are invalid.

No the mass in definitely not moving at the speed of light; nothing with mass can move at the speed of light. E = mC² is an identity; it says that matter is just another form of energy and vice-versa. E = mC² can be written as m = E/C², because the equation is reversible -- that is to say; matter can be converted into energy and energy can be converted into matter. Physicists who study subatomic particles do this everyday in atomic colliders. To their frustration, they cannot control what matter gets created from the energy released by the collisions that they create.

E=mc² simply means if you have an object, the object is actually made of a huge amount of energy.

To work out the amount of energy you plug the numbers into the formula.

Volume has nothing to do with it.

Try the video.