Actually, Pharisaic Judaism has its roots deep into the first century or two BCE, during the Second Temple Period. There were already differences of practice in the Second Temple from the First, and by the first century BCE, many changes began evolving due to corruption in the Priesthood, first at the hands of the degenerating Hasmonean rulers, then at the hands of the Herodian puppet kings of Rome, and this corruption was widespread in the Sadducee movement of priests.
The evolution of Second Temple Judaism into Rabbinic Judaism was difficult due to the loss of the Temple, but not a complete innovation-- rather, it was a transformation, with the Pharisees and the Rabbis who succeeded them taking familiar ideas, concepts, and practices already being done, and reshaping them into the core of a Judaism without a Temple. The idea of an immortal soul and an afterlife seems to have already been in play during the Second Temple period. And they remained in Rabbinic Judaism, which is why today's Jews for the vast majority absolutely do believe in an immortal soul and some kinf of afterlife.
Josephus has nothing to do with Pharisee religious leadership. He was a mid-level military leader who became a Roman apostate. He had absolutely zero religious significance or authority. The elite Pharisees were not mostly killed in 70 AD. Many died in that siege, but by no means all, and the Sanhedrin had already been removed from Jerusalem to Yavneh. The Pharisee elite at that point simply continued training others to follow them, the only difference is that by that generation, we no longer called them Perushim (Pharisees) but Tannaim ("Teachers" or "Repeaters From Memory").
Absolutely incorrect. Modern Judaism is the evolution of Pharisaic thought. It is entirely free of Sadducee influence. The major Rabbinic centers after 70 CE were not Egyptian-- Egypt was not a major center of Jewish thought until a thousand years later. The major centers of Jewish thought immediately following 70CE were Yavneh (Jabneh or Jamnia) and Tzipori (Sepphoris), and within a couple of hundred years, the greater centers of Rabbinic thought established in Babylonia.