Crack Enemy Communications: At the beginning of the game, choose a team ability that an opposing character can use that isn't a Wild Card team ability or a team ability a Wild Card can't use. Friendly characters can use that team ability this game in addition to their other team abilities as long as Cypher is on the map.

What happens if the opposing character with the TA Cypher chose is KO'd?
Nothing. The only condition that prevents Cypher's team from using the selected TA is if Cypher is removed from the map.

Can Cypher choose an ATA?
ATAs (like Runaways or Alpha Flight) are still team abilities, so Cypher could indeed choose them.

What happens with the Thunderbolts ATA? Can Cypher use Thunderbolts and choose his own Marvel TA? The Marvel TA selected with Thunderbolts by the opposing player? Both? Something else entirely?
The Marvel TA gained via Thunderbolts is selected before Cypher can choose a TA. So Cypher can select whatever TA is chosen by the player using Thunderbolts (say, Ultimates, for example), but Cypher can't actually choose Thunderbolts itself (and get to pick his own TA). (changed 6-11-11)

What happens if each team is playing Cypher? Who picks first?
The first player would choose first, then second player, and so on until all players using Cypher have selected a TA. (added 6-11-11)

If more than one player is player Cypher, can my Cypher (I am player 2) select the TA chosen by the other Cypher?
Sure. All Crack Enemy Communications requires is that the TA in question be usable by the other team; they do not actually have to possess the TA. This means that when player #1 chooses one of your TAs (say Mystics), now his whole team can use Mystics... and since they can uses Mystics, your Cypher can choose that TA, too, and now your whole team also can use Mystics. (added 6-11-11)

Updated. Please note that these clarifications are not yet in the PG, but they will be added with the next release. For now, here they are in black and white for your reading pleasure.