So when a hero of time travels back in time, is that version of them that traveled back now permanently separate? For example, when Dave traveled back to stop whoever from stealing Rose's journal that contained the First Guardian code. Was that death experienced by a Dave that had completely severed connection to the one that discovered the dead body? Or was that one just the Alpha Dave, in a sense, and the memory of the death was discarded?

If they traveled back from a doomed timeline then yes they’re permanently separate. But if they traveled back from further down the Alpha timeline then they’re fine.