I am an Ashkenazi-Levite Jew, and in my experience and to my knowledge, there is no 'pure' Jewish 'race' or nation.
Ultimately though, the two things everyone have in common are being human and descended from Adam and Eve.
Jews have DNA from many nations as we were scattered throughout the world, as indeed are many peoples. Judaism is a religion that can be practiced by Jew or Gentile; Gentiles can convert to Judaism, and are seen as fully Jewish, but Jews are not strictly speaking one nation, as we are a mix of many and all nations. I am sure that many Jews are descended from the Khazarim, but Jews are a mix, and not a singular 'race'.
Sorry if I can't reply in this thread; I see a box at the top saying something. Sorry also if my post isn't clear, correct or is insulting, none of which are my intention to cause.