Your text in color.

The basic premise that I have is that the Earth's atmosphere is accumulating kinetic energy not only from the suspected greenhouse effect but also from the various fission byproducts that have been spread into the atmosphere by human activity.

Do you even know what "kinetic energy" is? It does not sound like it.

If a fluid, such as air, is heated, or receives additional kinetic energy from any source, it will expand, (provided that it is not in a confined area) when a fluid expands its density decreases.

Is that supposed to be news?

What will happen if, by whatever means, the total atmospheric kinetic energy increases?

The atmosphere is in dynamic equilibrium with the Sun as primary heat source (along with tiny amounts of geothermal heat) and the cold of outer space as heat sink. Hence, energy can not accumulate at all unless either thermal absorption or radiation changes.

According to the laws of physics, the atmosphere will expand and push further into space. If such expansion is great enough, it may affect the low Earth orbit satellites that may drop out of the sky before their time.

Can't happen as I have just shown.

IF the atmospheric pressure or weight decreases, then the pressure that exists within the Earth will tend to bulge the planets surface. This bulging force will in return cause effects such as earthquakes and volcanos to become more frequent and violent. Perhaps over thousands of years the earth will expel enough gasses from its interior to again balance the weight/pressures.

The total pressure exerted by the atmosphere is quite small compared to gravitational pressure from overlying rock strata. No significant expansion is therefore possible even if the entire atmosphere were to vanish.

On top of these beliefs I believe that the use of nuclear power by many countries has been in a manner that is irresponsible and the resulting exhaust (radioactive pollution) from the use of nuclear power may be causing changes in the atmospheric conditions.

Heat from nuclear waste products is trivial compared even to geothermal heat, which is in turn trivial compared to the Sun's input. Forget it completely.

The physics part comes mainly from the Bernoulli's equation which states that, p + qv2/2 + qgy = constant.
where p is the pressure, q is the density, v the velocity and y the height in a gravitational field of strength g, all measured at the same point.
According to the laws of physics, lowering of the atmospheric pressure would cause greater evaporation rate.

Average atmospheric pressure has not changed by so much as .01 % in the past century. Hence, no such effect is possible.

Hence, your post is scientifically incorrect. You are presuming effects many orders of magnitude larger than the causes that you cite can produce.