That's irrelevant. It's like saying that you can count to infinity if you never stop counting ... but no, every number in the count is finite.

That's how limits at infinity work.

No, it certainly isn't.

You seem to be positing that Maxwell's Demon can be reassigned to another impossible task, but that isn't a proper use of his "powers".

Infinities defy simple assumptions about maths, while Maxwell's Demon only needs to ignore the Laws of Thermodynamics.

I'm being serious, not glib, here. "And then do it infinitely many times" doesn't automatically enable any possible outcome, any more than the "multiverse of all possible outcomes" enables hot dog fingers on Jamie Curtis.