Johannes,

I'm not an atmospheric scientist. You ask alot of questions that I don't have and am not able to find direct answers for.

Such as....

I would like to know what that "trivial number" is, also I would like to know if that "trivial number" is increasing or decreasing over time, or alternately if it would be possible to 'compare' that number to an amount that occurred before the 'nuclear age'.

I'd say it's modulated by solar activity and not by human technological capacity as in this case we're talking about loss by solar wind sputtering. In the case of Mars, it probably removed a good portion of it's atmosphere due to the lack of a global magnetic field for the last 4Gy.

[yadda yadda yadda]
what happens to the energy of the alpha, beta, and gamma 'particles'

We'll, like you suspect, the energy by one path or another is converted eventually into heat. Remember though, it would be a trivial ammount unless you live on Metaluna.

Alphas(He+) and betas(e-) are charged particles and therfore don't make it very far without interacting with something in the atmosphere, usually releasing a photon that is almost as energetic as the particle used to be. As for neutralizing, it's not hard for free electrons(technically a beta but with a trivial fraction of the energy) to adopt or be adopted by a local ion.

Gammas will interact with matter but remember, not necessarily locally. Gamma rays from underground nuclear explosions can be detected from orbit.

It's a long road from gamma to IR photons in a gas, many different possible interactions. The point is, it's not alot of energy being spread over a large volume resulting in a negligable energy input compared to other sources.

I would be very pleased if you could answer some questions about the 'radiation' that comes from the radioactive elements that are in the atmosphere.

Me too, like what are these radioactive elements. Just isotopes of oxygen and so forth or what? What are you concerned about in particular. Be specific.