Say I run Madrox (Giant-Size X-Men #001) in a 1 vs. 1 game and his SP activates, bringing an addition Madrox into the game:

"THE MULTIPLE MAN: Whenever Madrox takes damage from an opposing character's attack but is not KO'd, roll a d6. On a roll of 5 or 6, you may place a (X) Madrox or (X) Jamie Madrox on the same click number on the map adjacent to this character."
Given that there's no build total governing the action pool, can I use both figures on my turn? Or would I have to choose only one of the available figures to take my action that turn?

Based on this line from the 1 vs. 1 rules, I think it'd be the latter:

"Players alternate taking turns, each taking an action with their selected figure."

Either way, I think I'm trying this.

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Do feats and ATAs count toward calculating victory points, regarding the points difference between KO'd and the winner?

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Can special objects with a point cost be used, given that there's no actual force to add them to? Can any special objects be used at all?

So far, we've essentially house-ruled that only standard objects be used.

As far as I know, the 1v1 rules are falling into the same category as Event Dials.

They are a fun scenario and will not be getting "official" answers.

In other words, play it however it works best for you.