*sees a Nightingale immortality post*
I hope you don't mind me jumping on this post four months late OP!
While I find the idea of Nightingale being a god/genius loci/old soldier fascinating and adore all the fandoms ideas and creativity around it (I was and am going insane about it as well), BA has kind of revealed some time ago (and I say this without any animosity whatsoever, since it's nothing that could be widely known!) that this is not what is happening. It has not been explicitly brought up so far in canon writing, and BA ofc continues to be vague, but he said the words and reading the books with the knowledge in mind, the hints are there.
BA has said in response to the immortality question during public readings that after WW2 - as we know also from the books - magic users and inherently magical beings and creatures all over Europe were decimated/genocided and therefore, magic - just by the process of life "happening" - was building up and up but no one was there to "convert" it. It goes in line with his worldbuilding of magic being just another form of energy, like thermal or kinetic energy, that roughly follows the laws of nature and more specifically thermodynamics. If there is too much of it in one place, it becomes unstable, and reacts to become something more stable.
After all those decades, magic was simply accumulated to a degree that at significant points or due to certain triggers (like, let's say, August Bank Holiday 1966, which Varvara mentions as the day she started to age backwards) it started to "boil over" - a pile of energy that got out of control and (I quote BA here) formed "crystals" to stabilize itself, akin to a chemical reaction.
In London, in one of probably many differently-flavoured instances, magic once stabilized itself by forming those crystals in living beings, and of course, it was attracted to stabilize nearby or within vessels which already had a connection to magic and, more importantly, were still using magic up = converting it to another form of energy, which helps stabilizing the magical energy superfluid = actively practising - e.g. Nightingale, Varvara.
This also explains some of the phenomena of magic "coming back". Its community has been decimated, magic itself depleted by being overused and moreover, used to perversion, for war and torture and horrific experimentation and death. But as a pure force of nature, it has recovered much faster than the living community and continues to boil over in specific and localized events (and not always necessarily leading to de facto immortality or de-aging in humans, I suppose, but also the rebirth or rise of spirits, ghosts, genii locorum...).
(See Amongst Our Weapons / Stone & Sky, Professor Postmartin seems to be just another "victim" of magic stabilizing itself in persons already close to it, even if he is not a practitioner himself - I think its hinted at pretty strongly that he de-aging as well).
The rest of what I'm writing here is pure speculation, but re: Nightingale and forgetting his past life and his memories getting out of order, I suppose that it is a simple biological consequence - as Walid says to Nightingale in the beginning of the "Miroslav" short story, his age and therefore his memories outspan the "design specification" of his still very human brain; that he doesn't remember like he used to is to be expected. Nightingale even adds to this in his POV that he fears it might be a symptom of his PTSD (memory issues being very common for all kinds of trauma). (Btw for all those who haven't, I very much recommend reading "Miroslavs Fabulous Hand", the short story is excellent and completely written from Nightingale's POV).
Why Nightingale de-aged to his wartime biological age and Varvara not - my guess is that the magic stabilizing in people simply leads to them de-aging to the point that has been of enormous significance to them in life, the point where they are/were mentally "stuck" ( @philcoulsonismyhero mentioned this in similar fashion in convo a while ago and since then I cannot unthink it ). For Nightingale, this is obviously the war. For Varvara, her present-time age adds up with her losing her husband 1963 (she was born in 1921, which makes her outwardly early forties/middle aged). The mental state somehow influences their physical bodies to de-age to that point. How? I have no clue, but the biologist in me screams something something spontaneous-induction-of-adult-cells-to-revert-to-stem-cells-like-rejuvenation.
The common denominator I see in Nightingale, Varvara and Postmartin is only that all three of them were soldiers and fought in a war, so mayyybe lots of contact with (magical) energy released upon point of death has to do with "where" the magic decides to stabilize, and there might be a link to old soldiers lore somewhere, but that is also pure speculation.
(And obviously nothing of this speaks against characters like Nightingale becoming a god/genius etc on top of it! However, I think it is unlikely that BA will go down this route - Nightingale is already very powerful as he is, and I personally like that he is this combination of a very much traumatized, vulnerable, fallible human (albeit long-lifed) but has this extraordinary prodigiousness in magic - again just subjective opinion).
