Can you use outwit to counter somebody else's outwit? For example, I use outwit to counter a running shot. Can my opponent then use outwit to counter my outwit and thus be able to use running shot?

Yep, once your outwit is outwitted they can use the power you outwitted.

Thanks! I was also confused by this line "A character using this power must be within range (minimum range 6) and line of fire to the target." Can you explain what the minimum range means?

The minimum range is for someone with a less-than-6 range...Like the Ant Man from wave 2 of Age of Ultron...He has 0 range, but 2 clicks of outwit...So he can outwit someone within 6 squares that he can see...

Thanks that was very helpful.