On the question of “real” Kohanim and Levites, I’m not an expert on the halachic issues, but as I see it there are too ways to think about it. One is that there is such thing as a “real” Kohen or Levite, and when Moshiach comes he will (assuming he has ruach hakodesh) determine who is a real Kohen or Levite. Another perspective is that “the Torah is not in heaven,” as they say, and Hashem considers anyone who has inherited the status of a Kohen or Levite to in fact be a Kohen or Levite, regardless of whether genetic tests shows them to have the DNA signature. It’s kind of like the situation with mamzerim — unless I’m mistaken, even if one “objectively” should be a mamzer, halachically one is not a mamzer until people actually investigate and determine that one definitely is a mamzer. (For that reason some, including major poskim, have in some cases advised against investigating mamzer status.) One place to start for the halachic issues is Berachos 47b, which I believe discusses the concept of a “pasul” Levite with a Levite mother but non-Jewish father — I’m not sure where else to look.
Aurora: Thanks for the info — sounds interesting. I never meant to suggest that most Ashkenazim are descended from converts — only that, according to the studies I’ve seen, a certain amount of conversion has taken place and measurably affected the Jewish gene pool over the generations (which shouldn’t be surprising since Jews have nearly always accepted converts and they can’t have all been killed or failed to reproduce). The idea, popularized nowadays by the anti-Israel crowd, that most Ashkenazim are descended from the Khazars or other converts has certainly been debunked.