Something apparently happened that caused Luka to want to revive Heinrich, which in turn fucked everything. The son and daughter are apparently going around, trying to make sure past events occur as they should while Reaper and White Rabbit are just simply trying to keep everything from exploding. Brynhildr is allegedly Luka's attempt to help all the past versions of himself, which explains her unquestioning submission to his "authority". It also explains that, if there is a paradox and all the Luka's are connected, why a math problem Ilias presented to test Brynhildr was so easy for Luka despite his otherwise dense behavior. Sonya is also part of the paradox, though acting more as a "janitor" for the affected timelines similar to how the named Apoptosis (non-companions) function. Basically, they "delete" timelines that are being polluted by other timelines in an effort to limit the damage to neighboring timelines and ultimately prevent a catastrophic failure across the multiverse.
Sonya dies in part 2, but another version of her is torn from a neighboring timeline. Her death is only known to Luka, as is her true identity. A working theory is that the main timeline was de-stabilized following the "death" of Ilias and sealing of the most powerful angels under her authority, which would in turn present a power vacuum since there was nothing to oppose the monster lord or her kin. Even if another angel rose to take Ilias's spot, they would be significantly-weaker and less-capable of exerting their own authority while facing pressure from monsters who might not feel inclined to try co-existence. With such a huge power vacuum coupled with the defiance some monsters had towards Alice herself, it would stand to reason that the hinted-at "extinction of Human's and Monsters" (A special scene from after you recruit the succubus idol in Paradox part 1. Promestein gives a presentation on how co-existence is a failed concept because monsters will inevitably give in to their baser instinct for sustenance and male Human's who choose to procreate with them will inevitably find themselves outnumbered) would be an inevitable reality. Also, we've seen that monsters who were sealed previously became unsealed soon after, which means a monster like Alice the 9th(?) could easily unseal herself and attempt a coup.