User blog comment:The Brave Wolf/Assassin's Creed: Origins - New Rumor May 9th 2017/@comment-5088097-20170509174549/@comment-2112031-20170514080537

It should be noted that the Assassins have had female members pretty much since their inception. Eve led them during the Human-Isu War. Other notable female members include Iltani, the Babylonian Assassin who poisoned Alexander the Great, and Amunet, the Egyptian Assassin who killed Cleopatra with a venomous asp. As for Masyaf during Altaïr's time, Maud, Altaïr's mother, was identified as a member, as well as his wife Maria, with the only initial objections being not about her being a woman, but rather that she was a former Templar. 

Most estimates of when exactly the Exodus is supposed to have taken place typically place sometime during the New Kingdom era (1550 BCE to 1077 BCE). Mythological events are always rather hard to place. And yes, Moses' Staff has explicitly been identified as a Piece of Eden.