If a character picks up the Cosmic Cube, and they already had either perplex or PC would they be able to use either perplex or PC twice?

Relic 4-6.
Character can use Perplex and Probability Control. Each time a character uses one of these powers, after actions resolve, roll a d6 that can't be rerolled. On a roll of 1-2, place the Cosmic Cube in the square that character occupies.
(This special object is Immobile and can't be destroyed. Once per game per character, give a character occupying this square a power action and roll a d6 that can't be rerolled. On a result of 4-6, place this object on that character's card. That character can use Perplex and Probability Control. When that character is defeated, place this object in the square they last occupied. At the end of the game, if an opponent's character has this object on their card or all of your characters have been defeated, your opponent scores this object.)

You can not use the same free action twice per turn.

It's not about the free actions. It's about this line in the Player's Guide:

 Game effects which grant the use or possession of another game effect have no effect if the recipient can already use the new effect.

Thanks guys awesome

Note that if a character's normal perplex gets countered, they are able to use perplex via the Cube.