For the Black Mage HP, it's likely not accurate, since the battle analysis that served as a source for the HP also included the Black Mage's shield (which doesn't count toward the Black Mage's base HP). Though I don't know how much damage the shield requires to be removed, I'm going to take Namu's values with a grain of salt.
From what I've seen so far they're pretty reliable source, but I'll check this site from time to time to see if things are changing. I've seen that p1's HP was added before I updated the info about p2 and p3 - what is the source of that? just battle analysis?
It was indeed Battle Analysis. The reason we have an idea of the Black Mage's HP is due to a hacker in GMS soloing him (he got permanently banned not too long after though). The thing is, the battle analysis also records the damage used to break the Black Mage's white shields. I do keep track of Namu's wiki from time to time, but I've noticed some inaccuracies here and there; sometimes I would send an edit request to fix the mistake if I'm 100% sure about it. Knowing how Nexon structures their boss HP, a good chunk of the time it's in an increment of 2.1 (2.1 billion, 4.2 trillion, 31.5 trillion, etc), though it's not always the case. Unfortunately, the WZ files don't show his actual HP, so we can't validate it that way.
Isn't there a chance that the shield being disappeared is some kind of anti-cheat system implemented within the boss?
If you see Dango's video here https://www.youtube.com/watch?v=SC2ywo9oFPA&t=73s at 1:36 you can see the shield disappearing and then the following message appears on screen: "Black mage has detected a negative energy. They're unleashing their true power"
That's a different shield; the white shield I'm referring to is in all phases of the battle and appears when the Black Mage uses certain attack patterns. He uses the white HP bar shield right before the disco ball shield disappears in that video, and it also factors into the battle analysis.