Are you trying to correct the university teachings that I linked? The speed of gamma radiation is the speed of light = c, because it can be regarded as consisting of photons. c2 is something very different from speed, as it means velocity of light squared. Alpha radiation is particle radiation, and of course slower. Beta radiation consists of positrons and/or electrons, which are lighter than the helium nuclei in alpha radiation, and has a velocity beween alpha and gamma. Sound is pressure variations, travelling as waves. Pressure has no mass, and so sound hasn't.
What do you mean by biological energy? Whatever you mean, energy has no speed in itself. A good example of that is a stone on a mountain top. It it perfectly still, but it has potential energy compared to a position in the valley below.
I don't like "all energy has mass". I prefer to say that "energy is, in some ways, equvialent to mass".
By saying "light is made up of photons which travel in waves." you confuse two ways of regarding light. Light can be regarded as a stream of photons, or as a waveform. Choose one at a time.