If I stretched a rubber band, will compression energy be stored within it?
It always makes me wonder....
They will be still be energy until it fails or breaks. You can shoot it across the room so that tells you there is an energy there.
Yes, it's presumably between the atoms.
The energy is tension, not compression.
The energy you are mentioning is the tendency to go back to the original position. it is called the restoring force in physics.