Photons have zero rest mass. But because photons travel at the speed of light, they do have mass.

The extra mass is the kinetic energy of the system. Energy is mass.

The energy we think of as heat is actually the kinetic energy of the motion of atoms. So the parts of the copper that are moving faster would have more of the energy than those that are moving slower.

You can look up general relativity and the standard model, both of which have been tested to a high degree of precision.

No, a short period of decreased warming does not disprove AGW. Solar output varies, so when solar output is low, we would expect to see decreased warming. Now an extended period (several decades) of little or no warming would disprove AGW. Let me know when that happens.

The comment one screen below (which is the only one I've seen so far that bothers to do the math) shows that the energy the Earth receives from the sun is equivalent to about 16000 tons of mass per year. Granted, it could be wrong, but you're not showing any math that demonstrates that it's wrong.

But not only the atmosphere is heating up. The oceans are warming. The warming is also causing ice to melt into water. And of course upper part of the crust will also heat up because the atmosphere and ocean will heat it. I would think that the total mass that has warmed is several orders of magtitude greater than the mass of the atmosphere.

Most of the mass of your body is actually the binding energy of the quarks and gluons that make up the protons and neutrons of your atoms. Energy is mass. Deal with it.

The energy released from fission is not instaneously released into the atmosphere. The energy goes through the Earth, which will act as a damper to even out fluctuations.

This is why the temperature in caves is relatively constant, at about the average temperature of the temperature outside the cave. Cave temperature does not shoot up during the day or even get much warmer in the summer due to fluctuations in solar radiation because of the damping effect. Science -- it does take the slightest bit of understanding and thought!

Energy is mass. E=mc^2 gives us the conversion factor between energy units (e.g. joules) and mass units (e.g. grams). If an object heats up, it has more energy, and thus more mass. If you want to find out how much more massive, you will need to do some math. You can see some in the posts above that seem to show that there is enough solar energy falling on the Earth each year that if the atmosphere is trapping just slightly more than it is letting be emitted into space, the mass of the Earth will increase by many tons per year.