Re: Conservation of energy
Compression and extension are electromagnetic phenomena at the atomic level. If the material is stretched, the atoms are further apart than the rest position, so the "spring energy" is electromagnetic potential energy. When the atomic bonds are released (because of the chemical reaction), this will be transferred into kinetic energy at the atomic scale (i.e. the atom will depart the surface of the material with significant additional velocity).
But recall: At the atomic scale, kinetic energy and heat are the same thing. Temperature is proportional to the mean square velocity of the atoms in the material.
Bulk material: Spring Energy => Atomic level: Electromagnetic potential energy.
Bulk material: Heat Energy => Atomic level: Kinetic energy.
Bulk material: Chemical reaction => Atomic level: Electrons changing orbit
Bonus: Hooke's law.
Springs are complicated - when a spring is under compression one side of the wire is compressed but the other is extended. Neither of these are linear forces, but all smooth curves are almost straight lines if you zoom in enough. The point of a spring is that very small deflections are added up over the length of a very long wire. This gives an almost linear effect.
Springs closely obey Hooke's law not because it is a physical law, but because they are carefully manufactured to closely obey Hooke's law.