2.2 Questions about the story

There are questions about the story that to me don't add up, to the point where the i don't agree with the whole cinema sentiment that people seems to have.

Can someone explain to me how Cartethyia exists?

Cantarella gives the power to of the second awakening to imperator and that give him controll over Fleurdelis, to strike at the imperator/threnodian. Was that strike that separated Cartethyia/Fleurdelis? Did i miss when they explain when it happen? Why didn't they show this?

Also when was the threnodian killed? When Fleurdelis died? If so shouldn't imperator die as well since she is the resonator of both? He wouldn't be alive to ressurect Cartethyia. If the threnodian dies because the shackle dies (whatever that means they didn't explain) why wouldn't the Sentinel die if they're anchor dies?

Personally i feel like these questions took enjoyment from the story and honestly the cutscenes themself because i was confused. When did the split happen? Why did it happen? Because cantarella? Did the powers of the second awakening give insight to this outcome?