[renormalised (Carl)]

M increases as we accelerate towards c because we are adding energy (E) to the system by accelerating it. M and E are equivalent, so an increase in E is the same as an increase in M. To achieve c would take an infinite amount of energy. Remember, this is not the rest mass of the object you're accelerating, this is the mass (M) it has relative to the motion it's undergoing. If you were to make an observation of this object as it passed by you, you would see its mass being equal to the object's rest mass multiplied by the acceleration it was undergoing. If you were to observe the object whilst traveling along with it, it would still appear to have the same mass as it had at rest. That's what they mean by Relativity.

Now, we'll look at the case of the photon. A photon is a particle/wave of light, as you would know. It can travel at the speed of light, "c", and only at that velocity (that velocity being dependent on the medium through which the light travels). The moment a photon is created, it is traveling at "c". A photon, as you would know, has a rest mass of zero. So, it has no mass. Therefore, even when a photon is traveling at "c" it gains no net energy therefore no mass....the only energy it has is the energy it was emitted at. So, if the body emitting the photons is producing radiation in the mm range, it produces microwaves. If in the 300-700nm range it's visible light and so on.

To answer the very basis of your question, E=mc^2 applies to your nuclear reactions in exactly the same manner as it applies to accelerating a particle in an accelerator. It's just a matter of different situations.