So technically, this includes FREE and no cost actions. So technically, as soon as you activate the FREE for this effect, you fail the primary condition and can never actually use this effect. Probably should be "no costed actions" instead, or at least "no other actions".

I think they intended to mean "no actions" before the activation of the power, but, as it is written, i think you are right....

Free actions are still actions.

No. This power reads FREE: if this character has been given no actions or only a move action this turn, make a close attack targeting a character that missed or failed breakaway. I don't know how you came to that weird conclusion but obviously this power lets you make a close attack; it wouldn't immediately fail because you were given a FREE to activate reversal. This is a common conflict of language vs intent, no point in trying to make something that was intended to work not.

It's not a weird conclusion, it's a straightforward reading of the power. I'm not trying to make something not work, I'm trying to point out an error in the wording so that it can be fixed, much like what was done not too long ago for Pulse Wave.

There's no error. Activating this as FREE wouldn't cancel itself out because this FREE doesn't resolve before the check for no actions other than MOVE.

You must give an action to activate the effect. Resolution of the action has nothing to do with whether or not you've been 'given' the action.
Just to be clear, I don't anyone has the idea that judges should rule this power does nothing. There are perfectly safe assumptions here. But, the wording should be cleaned up.

Sassamo is 100% correct here. The technical wording of Reversal is flawed, regardless of how obvious the intent may be. Your argument is wrong.

It's an easy fix:

(...) If this character has been given no actions or only a MOVE action this turn, FREE: make a close attack targeting a character that missed this character or failed to break away from this character since your last turn.