What makes a photon a photon? As i understand photons are excitation of the electromagnetic field. Therefore charged particles are affected by this excitation. But what if we have (highly theoretically) a particle that has the exact same properties like a photon (spin 1, no electric charge, no color charge, no mass etc.) but is an excitation of an other field. Is this even (again, theoretically) possible? Is a particle with the properties of an photon always the excitation of EM fields? And would this photon-like particle interact with charged particles (because they are not belong to EM fields)?
 A: I think the existing answers are already excellent. I wish merely to add that this kind of question is one which is asked in theoretical physics all the time. Whenever we have some aspect of physics which seems to show something not accounted for in the Standard Model (dark matter is an example) then one thing to try is to suggest some new field. The apparatus of field theory allows one to 'cook up' a field with whatever properties you think worth trying (e.g. zero mass, no coupling to electric charge, but with energy and consequently gravitation, and possibly other couplings). If the field is in all respects like the electromagnetic field but without coupling to charge, then clearly it is not the electromagnetic field. But it has to couple to something or it will have no impact on the physical world.
Existing experiments rule out many such fields right away, however. If your field couples to $X$ then it will contribute to decays of particles with $X$. Measurements of those decays put quite strict limits on the possibility of further fields.
A: A very general principle in quantum mechanics is that everything not forbidden is compulsory. For example, any decay process that can occur without violating a conservation law should be one that actually occurs. The reason the photon is stable in the standard model is that for kinematic reasons it can't decay into multiple photons (like a jet in QCD). If you have a second photon with all the same quantum numbers as a photon, then it can decay into a photon and vice versa. Based on Lorentz invariance, the half-life is proportional to energy. (Re decay of massless particles, see Fiore and Modanese, "General properties of the decay amplitudes for massless particles," https://arxiv.org/abs/hep-th/9508018v4 .) So in this situation I don't think there is really any meaningful distinction between the two particles. You don't have any observable that can tell you which one it is, and the decay from one to the other can happen at any time and is impossible to detect.
If you think of the photon as the gauge boson corresponding to the charge of fermions, then its properties are fixed by that. You can introduce a whole second gauge, which then gives you the dark photon. But in the scenario you're talking about, the dark photon has no mass and no mixing, which means it can't be absorbed or emitted by matter. That means it wouldn't be observable by the types of laboratory experiments described in the WP article. But more than that, it wouldn't have been emitted in the early universe as part of the CMB. Therefore it wouldn't even be possible to detect it through its gravitational effects.
A: Simple answer: Yes. It's possible to have 2 different types of photon where only one type interacts with the electron and the other type doesn't. In our universe, however, there doesn't seem to be this other type of photon.
