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This makes me wonder what effect absolutely zero radiation would have on an individual. And on a population (e.g. would evolution be harmed by having no radiation at all?)

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I would say that ionizing radiation isn't the cause of most genetic mutations. It is just too rare and most of it doesn't penetrate the skin anyway, the rest has to be really lucky to hit the cell in the right place at the right time.

DNA copying not being perfect would be the main cause in my opinion.

There is one error on average for every billion pairs copied. The human DNA has 3 billion pairs. So every time a single(!) cell is copied, three mistakes are made.

You don't need any radiation for evolution.

But why are those mistakes made? Radiation?

It certainly could be, but I think most mistakes are made because of how the process is 'designed'; sometimes an incorrect molecule jiggles (literaly) into a place where it is improbable that it should.

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