His effect sais that if Wolverine would become stunned you could exaust and move him to the back row. Can you do this while attacking?

I know he is already exausted but some effects for exausting thing can be used on already exausted charactors.

Yes you can. Exhausting him is not part of the cost but is the effect. When effects, you have to satisfy as much of it as possible when it resolves. So even though he is exhausted and would become stunned, you only have to move him to the support row

Sweet

Hmmm, how confusing is that. Since the cost is actually discarding an X-Men card that does make sense I suppose, but it certainly doesn't seem intuitive.