Iconic Peppered Moth - gene mutation found

But if this is a dominant allele the black moths wouldn't show up 'from time to time'. They would, of necessity, need to be present in every single generation. And they would be selected against - a dominant allele which is selected against will vanish from a population much more quickly than a recessive one, since any individual carrying the allele is subject to whatever causes the negative selection pressure (in this case being easier to eat). You don't need the exact same mutation. I imagine something like being black can be acheived in a huge diversity of ways. For a similar example in humans, we can see that Europeans and east Asians have light skin due to different mutations. In both cases people moved to higher latitudes where lighter skin would be beneficial, and in both cases a mutation arose which caused lighter skin, but it was not the same in each case. The specific mutation selected for was the one which happened to come along at the right time. The same is true of lactase persistence in humans, northern Europeans and east Africans both evolved lactase persistence independently and the genetic basis is different in each case.

Yes, but it didn't have to be that mutation. If another mutation causing dark pigmentation had arisen in northern England, we'd be talking about that one instead. The point is that there are many different random accidents that can have the same effect. They don't come along only at just the right time. Some of them crop up at the wrong time, but then since it is the wrong time they are selected out of the population. If Adam and Eve were diploid, like all mammals, then they had no more than four alleles at any locus - two for Adam, two for Eve. And yet we know that there are hundreds of different alleles for some loci in modern humans. Mutation is a requirement of Biblical literalism.

She can't have been an exact clone, on account of being female. We need to allow some God-magic in the crafting of Eve's genome.