how does the wildcard ability works? I know they can copy any TA of your team... but when?
can my spidey copy jla to move for free... and then when he finish his move land in an object and copy the batman TA to be stealthed when my opponent attacks?
and... can taskmaster copy ultimates to shoot through stealth, and after he do that copy defenders and rely on another defender defense value in order to be safer when the other player attacks?

Like this:

Once per action, each of your Wildcards may pick a team to copy. They continue to copy that TA until you change it or until all legal sources of the TA leave play.

So, yes, Spidey can JLA free move, switch to Hydra to help an ally, then change to the Batman Ally ability when someone tries to shoot him, then switch to Mystic when somebody tries to hit him up close.

...so long as it's not the same character trying to hit him up close as was trying to shoot him...

Did this change recently? I thought you could only change once per turn.

I don't think it has ever been only once per turn, even back during Infinity Challenge. Anyway, since you asked, here is the current wildcard rules straight from the Danger Room rule book (Pages 14 and 15):

Wild cards. Wild card team abilities are special team abilities that allow a character to use any team ability possessed by any friendly character on the battlefield.
A character with a wild card team ability is called a “wild card.”
When making use of a team ability it does not possess, a wild card does not gain the team symbol of the team ability used.
Wild cards may use only one team ability per action. During your turn, you must declare any change in the team ability used by a wild card when you declare an action. During an opponent’s turn, you must declare any change in the team ability used by your wild cards after your opponent declares an action and before the action begins—for example, after an action is declared but before an opposing character moves or attacks. A wild card retains the team ability it last used until it uses another team ability, or until the end of an action in which the character whose team ability the wild card is using is knocked out or otherwise removed from the game.
If a team ability used by a wild card after the declaration of an action makes the declared action impossible to perform—for example, if a line of fire for an opponent’s ranged combat attack can no longer be drawn to the wild card due to the team ability now used by the wild card—treat the action as though it was not given and choose a different action instead. The wild card, however, must continue to use that ability even when a new action is declared.

Basically only One per Action. You may copy more then one TA per turn.

The big change was how WC works if you use it to prevent an Action from being legal (aka using Batman TA). Basically in that scenario you can not switch until a legal Action is completed.

Example:

1) Gorrilla Grodd attempt to blast Cosmic Boy.
2) Cosmic Boy copies Batman TA (attack is illegal)
3) Solomn Grundy then swings a tree trunk at Cosmic Boy
4) Cosmic Boy wants to switch to Mystics but can not since no legal action has transpired since he last changed TAs
5) Grundy misses (it really doesnt matter wether he hits or misses, but for Rokk's health lets say Solomon misses)
6) Black Manta wants to trident stick Cosmic Boy
7) Cosmic Boy can now switch to Mystics.

Wow, thanks. My venue has been playing it all wrong. They have told me countless times that I can only switch once per player turn.

This is not quite accurate,:disappoin the WC is only locked into the TA choice if the same figure (the one who's action was made illegal) is the one taking the "next" legal action (which is really the same action more or less ), not as you suggest, until a legal action is completed. To clarify, in your example Cosmic Boy could change TAs (to Mystics or Alt F4 say) in response to Solomon Grundy swinging a tree trunk at him, he could not however (assuming Grodd could Charge) change TAs if Grodd used Charge to move in and make a CC Attack in lieu of the (now) illegal RC Attack that was originally attempted.

BoT