What is energy seems to depend on what you mean by "a particle". But as I think I understand it, every particle in the SM is a form of energy, it's an excitation of a field which "has" energy in it. So if you say an electron in a potential well oscillates at discrete energy eigenvalues, you also mean they emit and absorb the difference in energy as photons. But no, photons carry energy, they also have "other properties". Yep, all the properties correspond to a quantum of electromagnetic energy with a definite frequency in the frame of some electron or other charged particle. It's essentially a chunk of U(1) symmetry. Why photons propagate at c (in a medium with only virtual particles in it) is a different question to whether they're a form of energy (which if every quantum particle is, then that follows). But photons "are" the energy differences in QHOs. This is one way to explain why photons are annihilated by an absorption mechanism. A single oscillator absorbs all the photon's energy (and the photon) when resonance occurs.