In most cases, yes...electrons, photons, or ions... that's basically what energy is on a atomic level.
Just... wow. Do I really need to explain to you what the difference between matter and energy is?
1) Electrons are not energy. They are subatomic particles (MATTER) with a negative electrical charge. Any energy attributed to them is in the form of their kinetic energy (motion) or potential energy, be that electrostatic, magnetic, gravitational, whatever.
2) Calling photons energy is fair, but I think it is stretching the definition quite a bit. I'd rather not be dragged down into a debate about why, so I'll just say "ok" and move on.
3) Ions are not energy for the same reasons electrons aren't. They are atoms with greater or fewer electrons than normal. Any energy attributed to them is in the form of their yada yada yada etc ad nauseum.
Energy, in the simplest possible terms, is the capacity to do work. Electrons and ions by themselves have no capacity to do work except via E = mc^2. Their capacity to do work comes from their relative motion and position within externally applied fields, electrical or otherwise.
As for "energy beings," Karajorma has already said that is largely a misnomer. What life requires is an energy gradient it can exploit. Everything else is just window dressing. Even carbon based life here on Earth exploits myriad gradients. Chemical is the most common, but thermal and electrical are exploited as well. The gradients inside a star are much steeper. I believe your argument is that there can be no cohesive structure inside a star. I disagree. It may not be solid, but there certainly is structure. The convection cells inside the sun are larger than our planet, but they are very much self-sustaining. For all we know, those cells could be older than our planet itself. In all that time, is it not possible that all that complex self- and externally-interacting electromagnetic flux could have become capable of the characteristics of life? Reproduction? You betcha. Homeostasis? Growth? Adaptation? Response to stimuli? None of these seem beyond the realm of plausibility to me.