Beyonder has this trait:

When it says that the Beyonder can "choose a standard power that any other character can use," does that mean standard powers currently showing on the dial or any standard power that character can use anywhere on its dial?

It means "a standard power any other character can use" at the time you give him the FREE.

"Can use" does not mean "showing on the dial". A character can use the powers showing on their dial, but they can also use powers from other game effects, like traits, equipment, effects from other characters, etc. "Showing on the dial" means the powers physically printed in the 4 slots on the characters dial.

So can Beyonder choose a power that the target character currently doesn't have access to, a power that appears on its dial but is not currently active?

Do you mean a power that has been chosen with Outwit?

In that case, no, because that power can't be used by the character.

Do you mean a power that the character has not activated this turn (ie, Perplex but that character has not been given a FREE to activate it)?

In that case, yes, because that power can be used by the character.

No, because that character would not be able to use that power at that time.

Pg. 28 of the rulebook-

"Can use" means that the figure can use it right now from whatever source.

If some figure has pulse wave on click 3 but they are on click 1 right now? That figure can't use pulse wave. When they get to click 3 then they can use pulse wave, but not until then.

Also, as noted, a figure can not use a power that has been countered. If you want Beyonder to be able to use impervious, for example, and you also want to outwit impervious on the only character that has it, then Beyonder needs to choose it before it is countered.

But if it's on their dial and not countered?
If they are getting from some other source (the Symbiote special object, for example, which lets a character use plasticity and shape change)?
Heck, even another player's Beyonder that chose a power that is no longer on the character that he originally borrowed it from (say, he borrowed it and then that character was damaged or Koed).

The character can use all of those powers.

Just to be clear, "countered" is no longer a term used in the game. I know what you are saying, but the new concept that "can't use" means you can't use it, seems clear enough. I don't know that it helps to reintroduce "countered" to explain it.

I think we need three more people to explain this.

(Kidding, thanks to everyone that has replied)