Re: Time Travel, I study a lot of quantum physics, so this may not be what mothy had in mind, but this is the way I see the time travel aspect, if it helps:
If Irina were sent back in time in the exact same universe, then Levia, Behemo, and the others would be gone, hence, “no Gods”. It wouldn’t matter where she got her prophecies from at that point – Levia would never tempt Kiril into throwing Elluka Chirclatia’s body into Sin since she wouldn’t be there, Elluka Clockworker wouldn’t exist, and a lot of events wouldn’t be able to go the same way simply because of their absence. If it was the same universe, there’d be a lot of souls lacking, as well, since they’d have moved on to the Fourth Period. I’m not sure how to think about that, though. In any case, things would be very different, but in my opinion, “Utopia” would still be quite out of reach.
If she were sent to another universe, it’s hard to say exactly how events would go, because we simply don’t have any information. However, the only souls from the “first” third period would be Irina, Adam, Eve, and Gammon. Levia and Behemo could exist in this universe, but if only four people retain memories of the first go-around, then the “karma of evil” will repeat itself, and everything will (presumably) turn out the same way, although, again, we don’t know anything about it since mothy hasn’t elaborated on it.
In terms of the “first” time around, I believe the Original Sin Story that we’re presented with, Maria Moonlit talking with Levia and Behemo for prophecies, etc. is the beginning of everything simply because of the “Clockwork Lullaby -Key of Word-” music video. The gears leading to the fourth period say “IV” for the Heavenly/Hellish ending. The gears leading to Graveyard ending says “III’” (three prime?), indicating to me that Banica’s events at least start in the original third period, even if they end up somewhere else. Finally, the gears leading to the Court ending say “III-2”, meaning to me it’s the second time around.
Sorry this is so very long-winded, but I wanted to give my thoughts. Hopefully it makes sense, even if I missed some details/something doesn’t work.
I’m not sure I entirely understand what you’re saying in your first scenario–You’ll have to forgive me, as I don’t study quantum physics.
How would Irina going back in time mean that the gods are gone? If she goes back in time, then she is, presumably, going back to a point in the timeline where the gods are present. Along with everyone else, as this would all be before the Fourth Period. I’m not sure how going back in time in the same universe could ever result in events that are different than what has already occurred. Unless you are referring to a circumstance where she is not actually going back in time (as it is seems your scenario involves the idea of a fixed chronology that cannot be circumvented that is independent of chronological events) but rather causing the Third Period to repeat itself, and are considering the Fourth Period to be a separate universe that everyone else has already left to.
Or to try and clarify my point, it seems you are saying that, if there is time travel, despite the Court ending taking place in the past it would still somehow be after everyone had left to the Fourth Period, an event that has yet to take place. This sounds impossible to me unless it is not actual time travel, but rather a reproduction of the Third Period taking place after the fact in a way that resembles time travel.
As for your second scenario my only comment is that Levia and Behemo would definitely not exist in the new universe. Mothy has already established that there are no gods in the Court ending. You’re absolutely right that the ending hasn’t been clarified much outside of a few details like that, so it’s hard to speculate.
I also generally agree with your third paragraph, though I disagree that Banica’s ending starts in the Third Period (I mean, yes it does start there as all the endings start there, but she does go to a parallel universe, which is what I think the III’ is meant to represent).
In general, interesting points. It’s a little sketchy though if mothy is following an established scientific rule system for how this is all working though. Things have been a bit soft-science up to this point.