Why does water boil easier in a lower pressure?
With less pressure at the liquid surface, liquid molecules find it easier to escape at lower speeds (Boil).

Why does evaporating water cause a cooling effect?
The higher speed (hotter) escaping molecules leave the cooler ones behind.

Why do the planets Mars and Jupiter have higher wind speeds in their atmospheres than the Earth?
I don't know, but my guess is that the thinner atmospheres have less inertia and can be pushed to higher speeds, all else being equal. (The upper part of the Jovian atmosphere we observe has a very low density. We can't see what's happening in the denser gas deeper down.)

Why does the high altitude "jet stream" move faster than the low altitude air?
I don't know, but see above question for my best guess.

Why does radioactive material heat its surroundings?
The high kinetic energy particles and quanta emitted by radioactive nuclei collide with surrounding molecules causing them to vibrate and recoil faster, which is defined as heat.

Is there more radioactive material in the atmosphere now than there was before our "nuclear age"?
Yes. But it is due primarily to nuclear testing, not nuclear power plants. BTW, this effect forces manufacturers of radiation shielding for low-level radioactivity testing gear to rely on metal stock forged prior to 1945, such as old battleship armor. Metal smelted since then is contaminated by low, but measurable levels of radioactive contaminants

If the kinetic energy of air molecules becomes extremely high, can such molecules escape the Earth's gravitational field?
Yes, that is why there is relatively little hydrogen and helium in the atmosphere. The oxygen and nitrogen molecules are heavier, and have a harder time getting up to escape velocity.