In short, it's less "having no heart" and more "having a damaged heart" for this one. It's why each of them are missing one emotion entirely, different for each person, like Sayo's lack of narcissism (self-preservation). There's a list out there on which are missing if you flick back to 14min into episode 1, where it's going through the different Elements, or at the text shown for each character in the opening.

The self-correction bit was mostly saying that it's easier to pretend that minor differences aren't there where possible, rather than to split a universe into two entirely for every small action. So Sayo's situation isn't quite a resurrection just now, it's the case of the universe trying to self-correct towards the "Sayo is dead" outcome while she is conceivably still alive, with perceptions changing to match that desired outcome like with what happened with the dismantling club incident in the past.

The universe split stuff is just the self-correction taking place on a larger scale again, as the Shadow Angel one is stated to be directly connected to the cast's universe - if they were to rejoin, like what's attempting to happen here, the universe would err towards whichever is the "bigger" one between the two, hence the attacks to expand territory. No details on why or anything yet, but I assume that if a fusion were to take place that the resulting universe would be "larger" as a result.

Yeah, this first episode is poised as setting up a lot of the shared Aquarion mythos stuff, like DAEVA, Vector Machines, Angels, a 12,000 cycle of reincarnation, etc for this series, so not knowing about that would certainly not help with first impressions.

No confirmation on how much prior knowledge will be needed for this one in general though, as while Logos was mainly sharing concepts, the other two are very closely linked, and the description on CR for this one seems to list all three prior series as having being things which have happened in the past here.