Out of the Shadows: Once per turn, when Batman occupies hindering terrain and is given any action that is not a free action, before the action you may place Batman in any unoccupied square of hindering terrain 6 or fewer squares away to which he has a clear line of fire.

How exactly is Out of the Shadows used? Can I say I am going to attack with Batman, reposition with this power, use Outwit, and then actually attack?
No, that's not quite how it works. To use Out of the Shadows: (1) Announce the type of
non-free action Batman will take, even if it is not a legal action from his current position, as long as it can be legally done from step 3. (2) Reposition Batman from a square of hindering terrain to another square of hindering terrain. (3) Perform the declared action.

So, using the example sequence in the question above, in step 1 you would say "Batman is going to be given a ranged combat action to shoot Superman, who is currently sitting over there near that patch of hindering terrain. Then you would reposition Batman from his current square of hindering terrain over to that square of hindering terrain near Superman. Then you would attack Superman once Batman is in place. You could not use Outwit after the placement before attacking because Outwit is activated by a free action and the placement of Batman is done immediately before he is given a non-free action (which in this case is the ranged comabt action). You are more than welcome to use Outwit before using Out of the Shadows (assuming you can draw line of fire from your current position) or after the action triggering Out of the Shadows is resolved... you just can't use Outwit while using Out of the Shadows.

Does Batman need to roll break away if he is adjacent to an opposing character when he uses Out of the Shadows?
No. Batman does not need to break away from an adjacent character. Out of the Shadows places Batman in a new square; it does not move Batman. Placement and movement are two different terms in Heroclix and placement does not require break away.