No, how life began is not part of the theory of evolution. It's true that scientists (especially biochemists) are trying to find possible pathways of how life could have started but this research is not crucial for the ToE.
Evolution only requires the existence of imperfect self-replicators but how they originated doesn't really matter because they are still imperfect self-replicators. In other words, the theory of evolution is a theory that is concerned with the dynamics of a system and not its initial conditions.
And wouldn't you expect to see transitional forms between the squirrel 'matryoska' descendents? I believe Darwin predicted that fossil evidence would be found to prove the transition.
Uhmm, not between the descendants but between the common ancestral population and its descendants. You have to remember that this is a branching process and once two populations become reproductively isolated there is no "link" between them anymore. Of course fossilization is a rare process, so you may not find a complete series of fossils.
Another way to visualize the speciation process is to take an image of the visible spectrum (e.g. from an old physics book for instance) cut it into two pieces of equal size and place them side by side:
At the left side the two populations are still pretty similar and able to interbreed. If you proceed further to the right they may still be able to interbreed but their offspring is infertile. Even further to the right they may not even be able to interbreed. Nevertheless, you have to keep in mind that this is a continuous process and there is no point where one species "gives birth" to a new species.