Yes, those would be examples of mutations. Mutations come in three flavors: good, bad and neutral...and those terms are dependent on the environment the organism lives in. The same mutation could be advantageous in a wet environment but disadvantageous in a dry one.
Whether a mutation is passed on depends on if that organism has a chance to breed. The mutations that are most likely to spark a new species are ones that offer up a significant reproductive advantage. A mutation that helps an organism survive longer than those without it, for instance, means that organism has more mating periods in which to pass its genes on.
As for your lady friend, I assume she has every opportunity to reproduce. So now the question is whether the mutation that allowed her to grow another finger is a mutation that exists in her gametes. Human evolution is a tricky discussion because we are a lot less subject to our environment than we used to be. Rather than adapt to our environment, we adapt the environment to us. Groups of people will very rarely enter into reproductive isolation for the long amount of time it would require for a new species to arise.
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