do a cards counter like +1 +1 or any counter go away when stunned

Nope. Counters only go away when the object they're on changes zones (thus becoming a different object), or if some power says to remove them.

Cosmic counters do ;)

counters stay inless cosmic or they say so

If through his ability, I have, say, 3 counters on Shinobi Shaw as he is visible, and I move him to hidden (eg. using Hellfire Club), do those counters remain on him? ie Is hidden a different zone?

Hidden and visible are both areas within the one in-play zone.

Right, thought so, always nice to check. Cheers