Spoilers
First off: Quadratum which the Master of Masters seeks is the realm beyond the Final World: The Realm of Death.
Just as the Underworld is the Realm of the Dead where Dead Souls go Quadratum is the Realm of Death where Dead Hearts go.
As for why the Master of Masters seeks the Realm of Death: he is enigmatic and as he says the Truth is in what you see not what you hear.
He could be seeking the Realm of Death out of curiosity or he could be seeking it out of fear of Death being a threat as great as Darkness or he could be seeking to kiss up to the Biggest Bad in the area in anticipation that the guy will unleash Noise to consume the Worlds to feed Death’s gaping hunger.
Luxu seems to have possessed Brain and sent him to the future using knowledge on how Maleficent got to the past and combined it with the Foretellers’ own technique.
It also seems as if Skuld is Xehanort’s Grandmother as Xehanort’s Mother resembles Skuld and yet has Xehanort’s Silver Eyes. Either Eraqus is Xehanort’s brother or he is Brain in disguise playing dumb thus explaining Dark Road showing a flashback to his past.
Of course Ephemer appearing to Sora as well as Subject X being a Girl with Black Hair indicates that Luxu ensured that both would go to the future while leaving their daughter in his care(naturally due to Luxu posing as Brain).
Seems Spirits are the result of Chirithy owners merging with their Chirithy. Nightmares of course are the result of Spirits falling to Darkness. The Master of Master of course phrased it as the owners of Spirits falling to Darkness turning Spirits into Nightmares while neglecting to mention that said owners would be merged with said Spirits!
The Heartless are a result of the 13 Darknesses being stripped of Bodies… What would happen if Maleficent got ideas and stripped the 7 Lights of Bodies? Light Heartless obviously!
Incidentally the 13 Darknesses each have their own fates: 4 Darknesses got stuck in the Data World as it collapsed, 1 Darkness merges with Ventus, 6 of the 7 Deadly Sins merge with the Foretellers and the Master of Masters and the remaining Deadly Sin Wrath is ravaging the Worlds in Dark Road and infects Xehanort with it’s corruption while also taunting Master Aqua in the Realm of Darkness. That leaves 1 Darkness unaccounted for.
The Deadly Sins incidentally didn’t target the right Foretellers aside from the Master of Masters(who obviously got infected with Pride): Wrath is causing terror in Dark Road and ultimately infects Xehanort(though obviously not attempting outright possession since it targeted Aqua) which results in it infecting Luxu while Aced gets possessed by Avarice, Ira gets infected with Lust and Gula gets infected by Sloth.
That leaves Ava to get infected with Envy(with Luxu assuming she offed herself for the sake of her role) and Invi to get infected with Gluttony.
Wrath is behind the Heartless outbreak(explaining all the violence they preform) while 1 of the 6 Darknesses that aren’t Deadly Sins is doing who knows what after being chased off by Luxu…