A Question for the Darwinian Proponents

Recently (for example, here and here) discussions of Intelligent Design have come back to the forefront. Now, as I have claimed earlier, I don't really have a dog in this fight yet, as I'm worrying about other matters presently (Christian Ethics) and haven't got around to backing any particular theory, because I don't think creation/evolutionary questions have a bearing on ethics. But in the light of these discussions, I thought I'd ask a "stupid" question. Those readers with some knowledge of genetics and evolution might help me out.

In standard darwinian theories of evolution, how exactly does speciation take place? A new species is distinguished by no longer being able to reproduce with the "old". I think that this is often because the number of chromosomes has changed. A human has 23 chromosomes, if memory serves. If a new species were to arise from us for example, with say 27 (i.e., not 23) chromosomes, exactly how might that happen? If one kid is born, with a misnumbered set of chromosomes, how does he reproduce and with whom?

We are also told, for example that the cheetah is endangered because the surviving members of that species have a very low level of genetic variability. Doesn't one or two members of a "new" species have that problem in spades. How do they develop the requisite variability?