1) While there is limited, recent evidence of regrowth, biology holds that the neurons you were born with are the neurons you die with. Women are born with every egg cell they will ever have. There is no total replacement. It's interesting that a philosopher would somehow touch on identity without touching on consciousness. Cogito ergo sum beyotch. 2) As a child of the southwest I can confirm that a river doesn't need a drop of water in it to be a river. It must merely travel a path from the head to the outlet without forking. Even that is often not enough and rivers end up with multiple names. The identity largely comes from navigability - "if we want to get from Ogg's village to Bogg's, we must float down the Trogg." 3) Jeron Lanier uses Theseus' Paradox to delve into AI and the Singularity. His conclusion is different than yours.
It should be noted that this does not hold true in the case of the hippocampus (memory) and subventricular (smell?) zones of the brain. Additionally, while the same cell may exist over the course of a lifetime, it still makes, strengthens, and weakens contacts with other neurons.biology holds that the neurons you were born with are the neurons you die with