"I’m still searching:
for anyone (or any place) that has information on how much radioactive material is in the atmosphere these days."

Don't know, but considering how much of it that occurs "naturally" I would say near the average amount that's "always" been in the atmosphere.

"Also I’m interested in knowing if anyone has made the connection that radioactivity in the atmosphere may be ‘heating’ (imparting kinetic energy to) the atmospheric molecules."

I'm sure it produces some heat, but it would be utterly insignificant compared with other factors (like sunlight).

"Then furthering that thought, I’m interested in knowing how fast the atmospheric molecules are moving in the ‘thermosphere’ and above it."

Fast. I believe temperature is over 2000 F.

"I know that any object that has the velocity of seven miles per second can escape the Earth’s gravitational influence."

Assuming this object doesn't collide with another object.

"I also know that radioactive decay of atomic nuclei imparts kinetic energy to the surrounding atomic elements; besides causing the surrounding elements to become radioactive."

Just, to clarify- radioactive material doesn't "grow" more radioactive material- a given quantity X radioactive material decays over time- over time less material becomes radioactive- otherwise our energy problems would be solved:)

"It has been proposed on this board that the Earth’s magnetic field will somehow prevent energetic particles from escaping the gravitational field of the planet."
No, you probably got this backward. Earth doesn't emit significant quantities of high energetic particles- the Sun and exploding stellar objects are source of these particles. The Earth's magnetic field deflects most of these particles from entering Earth atmosphere- the magnetic field also traps these particles (Van Allen Belts).

"The implication seems to be that radiation, man made or natural, including the VanAllen belt has no accelerating influence on the activity of air molecules."

Aaah.
Van Allen belt start at about 1000 miles up- beyond Earth atmosphere which "ends" around 600 miles (or could be km, not sure).
And radiation man made or otherwise shouldn't have any significant affect on accelerating air molecules.

"I’d like to know the basis of the conjecture that magnetic fields can prevent energetic particles from moving faster than seven miles per second."

They don't stop, they bend the path of high energy particles- and the speed can be much higher than 7 miles per sec- some approach the speed of light.

"As I understand it, the Sun has a greater escape velocity than Earth and there are magnetic fields associated with the Sun, yet it is able to expel massive quantities of energetic particles into space . Why could this not happen on Earth?"

It could (see above- Earth isn't a source of high energy particles)

"So far I have found many interesting and informative web sites; non of which give the information that I need."
Try this:
http://helios.gsfc.nasa.gov/cosmic.html
or go to Google and search "cosmic rays"
http://directory.google.com/