What happened to the Master of Masters? Who is he? What's in the black box he had?
As of now, IIRC, there aren't answers to any of these questions.
Why did the master of Masters leave the apprentices? If he has a keyblade that let's him watch them why didn't he come back when they fractured?
The Master of Masters fully intended to allow the events his all-seeing eye foretold to play out, for unknown reasons.
Why does Kairi's heart leave her body in KH1? Clearly after that door was opened her body wasn't destroyed.
I'm not actually sure what the answer to your question is, but...
Kairi is a Princess of Heart, so she doesn't have darkness in her heart like other characters do. So the rules that normally apply when people lose their hearts don't function in the same way with her.
How can Naminé and Roxas seemingly exist at the same time as Sora and Kairi who both seem to be conscious and active shortly after their creation? The other apprentices of Ansem went dormant when their nobodies were made.
Namine and Roxas were born when Sora released Kairi's heart from within his own and became a Heartless. Because Kairi's heart was within Sora's, releasing it created an unusual Nobody (Namine). Because Sora managed to regain his human form shortly after losing it, Roxas continued to exist, but without any of Sora's memories (unlike most Nobodies who retain their previous memories).
If Naminé is connected to Sora and that's why she can modify his memories how can she also modify Donald and Goofy's?
Namine can also modify any memories that involve Sora, no matter who they belong to.
How was Xion created? If Xion is a counterpart for Roxas and is controllable when why bother with Roxas at all? Why not just kill him and let Xion replace him?
Xion was created by constructing a replica of Sora's powers, based primarily on his memories of Kairi. (She's a literal manifestion of "my friends are my power!")
The Organization was actually willing to allow either Xion or Roxas to do away with the other, as long as it meant one of them surviving.
Why does Maleficent seemingly always end up helping Sora in KH2 when they were enemies? Is she some sort of anti-hero in this?
Maleficent has a stake in defeating Xemnas, since he keeps sending Nobodies after her Heartless.