A photon is the force carrier of an electromagnetic wave and it consists of an electric and a magnetic field propagating through space at the speed of light in vacuum.
It exhibits wave-particle duality and does not interact with another photon. The fact that it interacts only with charged particles also implies that it does not interact with magnetic fields.
A photon has an entourage of electrons and perhaps other stuff around it and, especially, in a particle accelerator energetic photons may collide in this way.
Q1. How is this possible?
Q2. Why do photons only interact with charged particles?
P.S: A picture is worth a thousand words: I don't have quantum physics background. I read Maxwell's equations and they only apply to waves. I peeked at Einstein's photoelectric effect paper but it only describes how light behaves like a particle.