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Yeah, that makes sense.
What better to make you harder than becoming the Ruler of Hell!

At the start no, but after being (essentially) left behind by Wolverine as Ruler of Hell for an undisclosed passage of time (a- time was different there anyway, b- we don't know how long Chaos...

I'd say it's the same Puck.
Given that Marvel timelines aren't always simultaneous my guess is either that

a) the Wolverine Goes To Hell storyline was before Chaos War and that Herc brought...