I had prob with Nightmare and used it, I was attacked and took damage which landed on another prob control. Am I allowed to use it? I am not probbing multiple times on the same click, it is a totally different prob control.

No, Probability Control is Probability Control even if you are on a different click.

There is no way around this either, since a character can not activate the same ability as a free action more than once. This matters because if you were to give Nightmare the Cosmic Cube and use his prob control, then take damage and end on a click without prob control, he still could not use the prob control from the relic.

Probability Control is not a free action (or action of any sort). You can still only prob once per character per turn. Quoting the power makes things much clearer.

PROBABILITY CONTROL Once during your turn, this character allows you to reroll one of your rolls, ignoring the original roll. A character using this power must be within range (minimum range 6) and line of fire to the character for which the original roll was made. Using the same rules, once per round during an opponent’s turn, this character allows you to force that opponent to reroll one of their rolls, ignoring the original roll.

I knew this and yet I still clumped it together with Outwit and Perplex as a free action. I am not sure why.

Just to verify I am understanding you correctly on this - an action token would be placed on the character that uses it, right? That's how we have been doing it, but wanted to double check this.

You don't place an action token when using regular Probability Control. You do it when you use the Theme Team PC.