Re: seems backwards
"How come the earliest start are labeled PIII and not PI?"
We thought all stars were like Sol and friends, the ones near us that we can take spectroscopy of quite easily. About a century ago, we found out that stars in Globular Clusters and the cores of what were then called "Spiral Nebulae" are systematically different from Sol-type stars so we then had "Population One" stars like Sol, Rigel, Sirius and the others in the spiral arms of what came to be seen as galaxies and "Population Two" stars that were identifiably different.
At the time, we had no idea what the reason for the differences was all we knew was that the stars near Sol and in the spiral arms of those Nebulae were of one sort and the stars in cores and clusters were of another.
As our Sol is *our* star and as its kind were discovered first, calling them Pop. I seemed sensible. The other lot, core and cluster stars were a *second* Population of stars.
It made sense at the time. It still sort of does. And, no, there will never be a need for a "Pop. Minus Five" when really, really new stars are born in milliards of years from now with exceedingly metal-rich bodies. Those will still just be Population I, like Sol.
So, Pop I: new, young, metal-rich stars, mostly in spiral arms. Pop II : older, metal-poor starts in galactic cores and Globular Clusters. Pop III: primordial stars, almost all hydrogen, helium and a smear of lithium; we have no idea where those will show up, not yet. Theoretically, Pop IV stars: born in the really promordial murk from fluctuations in the opaque chaos before the universe went transparent, not really "stars", more like very large bombs. Pop. IV stars would be extremely metal-poor, too and would help to seed the cosmos with heavier elements when they blew up. They might also produce shockwaves in the medium to initiate the condensation of galaxies, galactic super-massive singularities and Pop III stars.
Pop IV stars are, of course, simply my conjecture, there is no actual Science behind them.
There could be Pop. V stars; stars made from stuff that existed before protons, that fuelled a Civilisation in the very first instants after the Cosmic Expansion and that created ripples in spacetime which allowed for galactic superclusters to form but those are truly SF.