New sites forming and new histfigs, yes. New births, no. It's not visible initially but when the worldgen ended in year 2, it is year 50+ and nobody outside player forts has birthdate after 2....(Of course, for worlds like archcrystals, void events like merchants and sieges will generate non-citizen histfigs with birthdates after that in player fort)
Population increases (and decreases) are shown in exported sites and pops .txt, which I compared.
Is anyone born a histfig?
That only happens when an event occurs. And there's less events going on during play than in initial worldgen. Depends on the population of your world but when your population pool has thousands of eligible pops who might go reclaim a site, the chances of it being a child are nil (so no-one for the first 12 years or so) and someone born recently, fairly low.
However, I will check this when I have a world going. One of my races has a very low max age, so would be the best place to spot a "new" pop becoming a histfig.
So, I've been working slowly through a world to check out this. Monitoring pops every year and checking for new histfigs who were born after play started.
Post-worldgen there aren't all that many events to elevate a pop to histfig status and pretty much all of them require an adult so it takes a while.
However in my current world I have a race of short-lived minotaurs. They become adults at 7 and die at 20. Each year, I've been checking pop figures (minotaurs are prospering, thanks to being terrifying, giant steel wielding beasts) and every year a few new adult gets promoted to histfig status to launch site attacks as part of the minotaur quest for world domination. In a couple of years, all minotaurs born after play started will be adults. A few more years after that and all minotaurs living pre-start will be dead (besides vampires, necromancers and werebeasts). So either all their civs will die out, the world will be run by the undead, or we'll see some new histfigs.
Well, that was the plan and I'll keep going. But just now I discovered the first post-start born new histfig. It's an "unnamed male horse".
This is a horse who has no relation to any of the sites I've played. Born in a hillocks in the year 194 (the year play started), attacked by some gobbos and killed in 198 (thereby being elevated to historical figure status).
So, creatures are being born and those born after start of play are being elevated to histfig status.
"unnamed male horse" is a bit crap though, so I'll keep going and witness what the new generation of minotaurs get up to instead.