Since we know that Aldebaran is involved in one of them we can assume that it either is
-The Identity of Pride
We know that Aldebaran is acquainted with the Witch Cult, it can be assumed that he possesses/possessed the Authority of Pride
-Priscillas extreme Luck
Priscillas is extremely lucky everything she does ends up being the best choice for her (Her Luck could be the Authority of Pride but that's just speculation)
-Why are people transported to the world of Re:Zero
We know that Aldebaran and Subaru were transported to the world of Re:Zero, it can be assumed that Flügel and the founder of Kararagi are from Earth but why do they come there, the reason for Subarus arrival in the world could be because Satella wanted to
My theories for the other mysteries are:
1.Hector, the Warlock of Melancholy what is his role in the story?
We don't know anything about Hector, we only know that he once attacked the Sanctuary but for the rest we don't know anything, we don't even know if he's still alive, for the rest of the Witches we know that Satella and Pandora are the only ones still alive.
We don't know anything about his alignment in the story whether he is a character, that would support Subaru or if he would side with the Witch Cult and Pandora or Satella.
2.The connection between Emilia and Satella/Emilias parentage