Jews: What is Jewish source/s of our understanding of souls?

Almost everything in these speculative matters is submitted to discussion and controversy in the Jewish tradition. Even the Zohar and may kabbalistic books have undergone severe criticism from other Jewish schools of thought, and this is a normal phenomenon, since Jewish tradition is not like Catholicism or Islam, with a set of dogmas which are never discussed but have to be admitted by faith. As for Kabbala, it may bear the influences of many philosophies and thinkers, but it is primarily Torah, Torah at its utmost level of sanctity and loftiness, and I think it is quite normal that the divine Torah encomp all kinds of human thoughts and conceptions. Three English-speaking specialists of Kabbalah seem to give relevant answers to your questions: Daniel Matt, who is the translator of the Zohar in the Pritzker edition of Stanford, Arthur Green, "A guide to the Zohar", Shaul Magid, who seems to be more a specialist of Lurianic Kabbalah ("From metaphysics to Midrash", Indiana University Press).