(Bolding mine.) I don’t think the assertion in bold is true. Having the requisite Y-chromosome just means that the person with that chromosome has a common male ancestor with Aaron, not that the person is descended from Aaron.
The “vice-versa” is true.
True, if Aaron had any brothers, or male-line cousins, or so on, they and their descendants would also carry that chromosome.
As with all things, it gets pretty complicated:
Of course, it’s also possible that Aaron himself was cuckolded and never actually had any descendants, and that everyone who ever thought they were descended from him was actually descended from some other guy. Or that such an event happened to one of his near descendants, and through random chance, that descendant’s purported line came to dominate the purported descendants of Aaron. With such an early non-paternity event, it wouldn’t matter how meticulous further generations were about paternity.
And an awful lot of ancient Jews must have converted to Islam and Christianity, and mingled with the rest of the population. To the extent that there’s genetic evidence of kohens having common decent, it would be truly shocking if you didn’t find the same genes amount other men in the middle east.
Interesting about the the Samaritans having priests who appear to come from a different line. That kinda matches the most plausible history.
To get back to founding a new temple, all you really need is a group of Jews who want to worship together. While it’s best to have a real Torah to read from, just a minyan (ten adults/men) allows you to do a lot you can’t do on your own, and there are definitely tiny congregations who are just ten guys who meet in someone’s living room.
(There are daily prayers that are supposed to be said publicly, so you need a minyan to do it.)
The next step up is to obtain a kosher Torah scroll. No, you really can’t write your own. Writing a kosher Torah is a highly skilled trade. You need to buy one from someone qualified to do it. But they are available. Expensive, but available. And you don’t need a new one, you might buy one from an old congregation that’s disbanding. With proper care and routine repairs, they basically last forever. (Repairs require training, too, but that requires a much lower skill level.)
Once you have ten Jews and a Torah, that’s pretty much it. It’s nice to have your own building, and an ark in which to store the torahs, and other prayer books, and seating, and hey, maybe even paid staff. But you don’t need any of that.
What’s very interesting is the Falasha Jews from Ethiopia that split off at least 1000 years ago. They look like the rest of the native Ethiopian population. Since they split off that long ago, they don’t celebrate Hanukkah and don’t have a Talmudic history. They faced pretty bad discrimination and all of them were evacuated out by Israel by the early 1990s under the Law of Return.
To bring this back on topic. They share a lot of genetic markers with the rest of the Jews and they have a priestly class that has the Aaron gene.
Sounds like the title of a book. Interesting!
Well, I only know what this seriously religious man told me.
Sasha Baron Cohen could be a kohain. But the name alone doesn’t make it certain. My best friend since I was seven has the last name Cohen. His father made it clear to him that however their ancestors got the name, they were not kohianim.
Conversely, (as has been mentioned) not all kohainim have the last name Cohen. A kohain is forbidden to marry a woman who has been divorced. If you take the first letters of the phrase ‘he who cannot take a fallen woman’ (I forget what language it was in) you get Kaplan. So alot of kohainim have that last name too.
There was a great episode of Millenium based on this. In order to keep a baby ritually pure and fit to become the new kohain gadol (roughly the high priest) of a rebuilt Temple, he was carefully raised in penthouse apartments and moved from place to place in helicopters. Lance Henriksen’s character, Frank Black explains (and this is entirely true) that various Christian and Jewish groups are working to rebuild the Temple. Some of the Jewish groups believe this will bring the moshiach who will fulfill prophecies, gather all the Jews ina restored kingdom of Israel, and usher in world peace. Some of the Christian groups believe that rebuilding the Temple will bring about the Second Coming. Other Christian groups believe (IIRC this is the premise of Left Behind) that the apparent savior who comes and unites the world will actually be the antichrist. But they also believe that the ascendancy of the antichrist will start the End Times and the Second Coming, rapture etc will follow.
I think the issue is, indeed, that the priest needs to ritually purify himself before he supervise sacrifices, but the ritual to do that purification needs to be done with a valid sacrifice (performed by someone who is ritually pure).
But i thought that the red heifer supplies a loophole, and that’s why they are trying to breed one.
This American Life did a piece on the red heifer.
I admit that it’s my primary source of info. But when it came out, i was working with a lubuvitcher, and asked him about it, and he confirmed the main points. He was fairly knowledgeable, although obviously not an expert in how to bootstrap the third Temple.
Huh, i thought “Kaplan” was just a version of “chaplain”, basically, a translation. 
I agree that a lot of families named “Kaplan” are also kohens. Like “Cohen” and “Kahn”.
A quick Google confirms that once again, I was in error. I am certain that a fairly common last name for kohainim came from that phrase. I shall do more Googling to find it.
ETA
it is not Katz. That is a German Jewish name for kohainim short for “Kohen Tzedek” meaning ‘priest of righteousness’.
I will keep looking.
I don’t recall that episode, but keeping the child pure until they reached adulthood would be the tricky part - from what I’ve read, even today, when there is no temple and no animal sacrifices that require ritual purity, it’s an Orthodox belief that a kohen shouldn’t even go into a hospital unless absolutely necessary, because they’d run the risk of being under the same roof as a dead person and that alone is sufficient to make one impure.
If I knew enough about the finer points of Judaism to do it properly I’d be inclined to write a YA novel about such a kid.
I have heard, yet at this point I have begun to fear that everything I know is wrong, that in Israel there are certain road signs indicating that kohainim should not drive further as the road goes through a cemetery.
It’s also discussed at length in Michael Chabon’s The Yiddish Policemen’s Union, where the protagonist stumbles upon a massive U.S.-funded military-training/red-heifer-breeding operation to retake Jerusalem and build the Third Temple - all unfolding in an alternate timeline where postwar Jewish refugees were given Sitka, Alaska instead of Israel.
The Jewish line of descent is matrilineal. IOW you’re Jewish if your mother is Jewish. Presumably because the only parent you can be sure of is your mother. Also, there’s no “half Jewish.” If your mother is Jewish, you are 100% Jewish.
The priestly caste, OTOH, is patrilineal - you are a kohen if your father was and if you’re male, because the priesthood is the specific domain of the sons of Aaron (or, assuming Aaron is a mythical figure, whoever the real Y-Chromosomal progenitor of the caste may have been). I’m not sure whether the daughters of a kohen can transmit kohen-ness to their sons, though, or what happens if your father is a kohen and your mother is Gentile.
If you are anticipating a new Reform congregation, you may want to check in at reformjudaism.org, the website for the Union of Reform Judaism. However, small congregations are becoming difficult to maintain. At the Reform temple my wife attends, the building and the Rabbi are shared with a much smaller Conservative congregation, which closed its synagogue several years ago due to diminishing participation.
Apparently, schools are turning out fewer and fewer Rabbis these days, and the URJ has very strict guidelines on who can be approved. It took my wife’s congregation two years to find a Rabbi to replace the man who was retiring. (We liked him. He was a tough act to follow.) It was a pretty good position too, but demand exceeds the number of qualified graduates, and they kept getting outbid.
Good luck.