And I am sure that you understand that a lit match can start a forest fire.

Bad analogy. A lit match is still not hotter than a forest fire. Maybe I should have said a penlight and a twelve-foot arc-powered searchlight.

Can you explain why a spent fuel rod from a nuclear power plant is more radioactive than it was when installed in the reactor?

This is hard to simplify. Radioactive elements decay naturally. Uranium in nature emits radiation and energy slowly for millions of years. In a reactor, this decay is "encouraged," and the energy is released over a few years instead. The spent reactor rods are still radioactive, but after reprocessing, will decay to near-nothing long before natural uranium will stop emitting.

I don't have a good analogy for it, but you can think of iron oxidizing as rust, versus iron burning in a sparkler. Same process, different rates.

The natural variations of the sun during one day or year still dwarfs the energy added by nuclear power and its products. Take the timeline out to decades, or centuries, and there's even more natural variation.

In short, nature's noise level far exceeds your signal, so there is no real danger of changing anything.

You aren't going to bust the Hoover Dam by peeing into the reservoir. Trust me. Even if the dam was full right up to the brim, you'd just have about a cup's worth of overflow. Don't let the EPA see you, though.