Vermouth and the Demon King of Destruction

So, I have read quite a few spoilers here and there, and I have a pretty good grasp on the outline of the story. However, there is a few things that I cannot find an answer for.

I understand that Destruction and Incarceration were former heroes who had defeated the ancient demon kings. Then, out of jealously, Destruction stabbed Incarceration in the back; Incarceration becomes a Demon King out of resentment, and Destruction also becomes a Demon King for some reason.

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I am also aware that Agaroth, the previous life of Hamel, managed to hurt Destruction in the past, and from it, Vermouth was born. Now, here is where my questions begin:

• Is this Vermouth, born out of Destruction, the same ancient hero that fought alongside Incarceration, or is he "someone" completely different from the two (original ancient hero and the demon king)?
• Why did Destruction even become a Demon King? Was he cursed by Incarceration?
• What were the actual contents of the promise? I know that Incarceration wished to die, but what, exactly, was the promise?
• Does Noir Giabella remember her previous life? Is she aware that Hamel was Agaroth?

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Also, I was re-reading the portion where Eugene visits Vermouth's tomb, and I noticed something. Tempest tells him that when Vermouth was about to deliver the finishing blow, he sheathed his sword and made the promise, since Incarceration would have killed the others.

Is this confirmed later on? Did Vermouth really have the power to kill Incarceration, but decided against it because he would need his friends? I know that they played important parts in the fight against Destruction, but how did Vermouth know of their potential?

And why was Agaroth reincarnated in an unfit body, and in the same era as Vermouth? Agaroth is from way before Hamel, no? Why did Vermouth only appear after Agaroth was reincarnated, if the blow Agaroth hit hurt Destruction right then?