First,
lets say I have a wildcard, a batman ally and a mystic. does the wildcard have just one of the abilities or does the wildcard have to pick one per turn?
second, I heard that fliers can carry characters. is this true? if so, how does it work?
thanks!

well things might have changed, but last time I heard it you would have to pick one TA to copy per action. but it could have changed to pick one TA per turn. sorry can't help you there

but yes Fliers can carry one person. it reduces their speed by -2 the trick here is lets say you have a flier with 10 speed and charge. he wants to carry a person and charge.
First you Modify your speed in half for Charge then you Reduce by -2 carry his charge movement ends up being 3.

That's correct.

From the rulebook, p. 18-19:
"Wild cards.
Wild card team abilities allow a character to use any team ability possessed by any friendly character on the battlefield. A character that possesses a wild card team ability is called a “wild card.”
When using a team ability it does not possess, a wild card does not
gain the team symbol of the team ability used. A team ability used via a wild card team ability can’t be used as a prerequisite for a feat (see Feats, p. 19.)
Wild cards can 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 defeated 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 opposing character’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."

And to further extend on vicious x's description of flyers:

Any character with the symbol has the Flight and Carry Ability.

Characters with the Carry ability can carry other characters with the or symbol. They cannot carry characters with , , , , or symbol.

When the character makes a move declaring he is carrying an adjacent character, he must reduce his speed by -2, and remove the character from the field for the duration of the movement. When the carrier ends their movement, the carried character is returned to the field and placed in an adjacent square.

Just to be comprehensive...
You also cannot carry , , and characters with Battle Fury.

So the flier does not get to make a free attack, correct?
does the character that gets dropped off gets an action or just the flier?

HE gets to do whatever he normally gets to do. Normally one does not get to attack after moving. When using Charge or something you do. Carrying would not change that.

Just the flier. (And the "passenger" cannot be given a non-free action after being carried.)