I am COMPLETELY confused about the wild-card team ability. How many times can i use it per turn? Also, what are the criteria for copying the abilities and when can i turn them on/off, switch to a new ability, etc? Help, please!

Secondly, I have a stealthed Green Arrow. I use the option of turning off his stealth so friendly Scarlett Witch can see him for a re-roll. I make the re-roll. Now my opponent's Destiny wants my Green Arrow to re-roll again. When he declares that, can i turn my stealth back on, eliminating Destiny's line of sight?

What about the Batman team ability? If i turn that off, when can i turn it on again or is it off for the remainder of my turn?

With wildcards, you can use any team ability that any of your figures have.

You can change once per action, and can never use two team abilities at once.

Stealth and Batman Ally TA stay off until the end of your turn, when they come back on.

fm

and those are the facts

And just to add, any optional power/ability that is turned off remains off for the remainder of your turn.

Your team members aren't stealthed from each other , unless some body changed it and didn't tell me .

They always have been. Stealth/BTA affects any LoF drawn to the figure through hindering terrain, no matter which force the figure belongs to. But voluntarily turning off Stealth/BTA until the end of the turn has always been an option, as well.