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1. DNA can mutate and cause large changes. Why do you think lions and tigers have so many similarities and differences but are the same species? Humans, even today, are still mutating. Dwarfs for example had usually have mutated DNA. This can even be passed to their kids to where they have it too.
2. Evolution doesn't say anything like that, but, if I remember correctly, the big bang theory claims that 2 particles collided with each other. This would be possible if there was nothing, because there would be nothing to stop them and each would have a tiny bit of gravity, causing them to come together.
3-A. Carbon dating isn't the only way to find out how old something is. Also, a volcano erupting wouldn't change an artifact if it was beneath the earth far enough. it could though, destroy rocks and soil above it allowing water and wind to expose it.
3-B. Like I said in 1. But still, fossils have shown early humans that appear slightly more ape like.