Why the repeated mention of time travel in the description of the Te Oria and the lost technology? It sounds like a huge Chekhov's Gun in the offing - the Te Oria gets triggered to destroy the world, so they Take a Third Option to avoid having to use the solution they came up with.
So what was with Faris going berserk and almost randomly killing the little girl?
She got tunnel vision.
It makes sense that the Big Bad arranged for the doctor and his two minions to get into the party, but wouldn't someone notice that the guy who attempted a coup d'état just a bit back was trying out h'ors d'oeuvres?
I think he had a monocle, so he was effectively anonymous.
If all they needed was for two people to have a near-experience with death, why not just fall off the cliff again and be saved by someone on the ground?
They seemed quite comfortable with the current situation in the end...
Near death experiences have an annoying tendency to become actual death experiences.
And if they knew it was safe, it would defeat the whole purpose, as their souls wouldn't jump ship.
When Falis ends up in Alita's body, why is she able to perform the exact same feats of badassery as before? Alita's body would have been significantly weaker than Falis'. Hell, Alita was exhausted just on the way from the castle to the forest. Yet as soon as Falis ends up in Alita's body, she's jumping around like an Olympic gymnast on speed. I know, I know... Rule of Cool. But still.
Alita's body may have a few secrets of its own, like how if overstressed, it can enter a berserk state. Falis states it never happened to her in her old body. And those natural red eyes aren't a common color at all, at least among humans.