Thoughts on Daemons
Remember most of the long-lived need not be famous or distinguished. An obscure person who's had an interesting career during their long life is as good if not better. However, men tend to be civil servants now to hide their identity, and women tend to be either civil service, teachers, nurses, etc. Genevieve Knight is a good example; she's long-lived and was born in the late 1780s and has worked as a maid in the houses of other long-lived people, shifting from household to household whenever needed. She is much sought-after since she runs households superbly well.
That's because there are very, very few of them. The actual frequency of the demonic mutation is one in 3.2 million births. However, that's only part of the story. Obviously, in societies where childhood deaths are high, many of the demons born don't survive birth or childhood and are simply just more babies that never made it. Also, the mutation itself doesn't kick in until later in life (early-middle thirties for women, late forties for men) so societies that have relatively low life expectancy don't generate demons simply because people don't live long enough to undergo transition. That's why demons from ancient times tend to be from the aristocracy and wealthy classes - their higher living standards meant longer lives so any demonic mutations that did show up had a better chance of being exhibited. That's one of the underlying threads in the stories, by the way, one of the effects of modern society and its extended lifetimes is that a much broader social spectrum of people is making it to and through the transition.
The final constraint here is the survival of the demons themselves; they aren't immortal. We've already seen or heard of five demons getting killed (Richard Soames, Rasputin, T.E. Lawrence, Bran, and Odin) plus three I've mentioned that haven't been in the stories (Julius Caesar, Commodus, and Caligula - the concentration in the Julian family is interesting). I'd suspect the average lifespan of a demon unassisted is around 800 - 1000 years, the ones we meet in these stories are the successful examples who have (by luck, skill, and mutual assistance) exceeded that.
We know his history from Messalina who saved a complete copy of Claudius's History of the Julian Family (and his other books as well; they're in the NSC basement. Robert Graves basically translated the history, re-wrote it in modern language and published it as I Claudius and Claudius the God.) Transitions can happen early or late depending on circumstances; there are some indications that severe physical trauma or stress can bring on early transition. Achillea went through a very early transition probably due to the wounds she took in the Arena. Caligula was another very early transition. In his case, it was brought on by a near-fatal illness from which he only just recovered. That induced his transition and, when he was told of the condition (probably by Claudius who may have been a short-lifer who knew the secret, Messalina has kept that to herself) he got a bad case of the God Like Delusions and sent him over the edge. That precipitated his final madness and assassination.
To give you an idea, there are about 15,000 demons alive in the world at this time.
The demonic mutation is a natural mutation that defies easy analysis. By the IH era, the presumption is that there are "master genes" that turn on and off whole clutches of other genes and that the demonic mutation is in one of those master genes. It's also mildly sex-linked, 2/3 of all demonic births are female and females have a more advanced version of the condition (the earlier transition and the red-glowing eyes for example). The actual mutation is very rare and is very recessive. Since demons can't have children, it’s not known whether the condition can be inherited. The only way to find out would be for two people who have the demonic mutation to marry prior to transition and have children. Since the mutation can't be detected prior to transition, the chances of that happening are very slight.
Having said that, the odds of a demonic mutation taking place can be affected by conditions. Rigidly static, socially immovable cultures reduce the chance of the mutation taking place (hence the rarity of the demonic mutation taking place in China or pre-modem Japan). Societies where the standard of living is increasing rapidly and there is a high degree of social mobility and cultural/ethnic mixture increase the probability of the mutation taking place. This doesn't mean that the mutation only takes place in those conditions or that it only takes place in one place at a time. It's occurring all the time, everywhere, just some places more often than others.
There's another theory and this is just beginning to circulate at the time of IH. That is that the demonic mutation isn't a mutation at all but that the demonic form is the "mature" form of the human species. This postulates that short-lived, fast-breeding humans like us are a sort of larval form of the human race and exist to spread the species as far and as fast as possible. Once dispersal has been achieved, we mutate to the mature form that is very long-lived and slow breeding. If we get to the point where another burst of growth and dispersal is needed, we switch back to the short-life form and start the spread again. Under this interpretation, Eldest is the lone survivor of the previous cycle. This theory, of course, remains purely hypothetical and unproven.
To some extent, the two previous answers have covered this. Other demons have formed and a few survive, but the problem is that in many cases, the conditions simply are not conducive to survival. In Africa, for example, the average life span was in the low thirties for much of human history (for women, much, much less due to incessant child-bearing). So there are essentially no demons there. However, there is a tradition in Africa of tribal mages and sages who were reputed to be very, very old so it's quite possible that some have formed and survived and taken on that role. South America is another case where conditions weren't that conducive to survival so few demons actually emerged. There probably are some but their numbers are way, way below average.
There are some in China, one might look suspiciously at monasteries and monks for example. Avoiding detection is a real problem in a hugely bureaucratic society.
On Concealing Long Lifers
With increasing difficulty is the obvious answer. Things like manipulating the witness protection program system, major forging of biographical data etc are partial answers but by the late 20th century, time was running out. This was a matter that was on the Seer's mind from around the mid-1950s onwards and it was becoming progressively more important as the years ticked by. The Conrad stories have this as a back-theme. By 2020-2030 the game was more or less up; then it wasn't a question of whether the Demons would be discovered, it was a question of when and how. That was when The Seer and Nefertiti had laid their plans for them to come out at a time of their choosing rather than be discovered. In fact, time caught up with them and the need to seek refuge from the spreading catastrophe of the Great Biowar meant they couldn't hide any longer. There was a window of opportunity when spreading despair would cause people to grab at any hope and any idea that there were "special" people fighting for them and brought a carefully chosen group of his people out into the open.
The one advantage that the demons had was that they didn't have to conceal their births, they simply had to conceal the fact there were no deaths associated with those births. That was what really put the 2040- 2050 era as the crisis, it was the point where people should have started dying and didn’t.