Do Alternate Team Abilities i.e. X-force count towards your 10% feat cap?

No. ATAs are no longer feats.

Also, it's good to remember that only figures with the prereq will possess the ATA, so if you have wildcards in your team that don't meet the prereq, those wildcards can copy the ATA as well as the normal TA's (as long as the TA/ATA permits wildcarding).

For instance with Outlaws, if you have that Spider-Man in your team, and you play an Avengers keyword team, Dr Strange, Iron Fist and Black Panther can use the ATA as well.

It's worth mentioning that some ATAs such as Squadron Supreme specifically state that Wildcards may not copy the ability.

ATA is Additional Team Ability. Can I only add an ATA to a character that have a TA printed on dial?

If I add an ATA Y who grants an abillity "YYYYYY" to a character that have a TA X that grants an abillity "XXXXXX". Is the result of the addition of the ATA to TA = "XXXXXX" and "YYYYYY"

If I have a character that have a TA X and a Keyword Y that let me use an ATA Y, can I copy both TA/ATA at the same time?

We'll use Fantastic Four and Fantastic Force as an example. Starter set The Thing would be able to use both the TA and the ATA. Now if you have Spider-Man on the team as well (the one without the Fantastic Four keyword), he'll only be able to wildcard one or the other at a time. So you'll have to say he's copying the Fantastic Four TA or the Fantastic Force ATA.

Now if the wildcard you're using has the Fantastic Four keyword, then they would gain the Fantastic Force ATA and still be able to wildcard another TA.

And no you don't need a printed TA on the dial to be able to use an ATA. Otherwise the Checkmate and League of Assassins pieces in Brave and the Bold wouldn't be able to use their respective ATAs.

ATAs are keyword based now. Anyone with the keyword can get the ATA, and unless it otherwise states it, you can also use any printed TA as well. You can only have 1 ATA assigned to your force though.

Technically it stands for Alternate Team Ability (see p. 17 of the 2010 Core Rulebook), but don't let the name confuse you. It operates like DFitz1138 and ChiRocker said.

And note that any wild cards with the keyword on your force must be assigned the ATA. So if you use the Fantastic Force ATA (prerequisite Fantastic Four keyword), and Secret Invasion Spider-Man is on your force, then he must be assigned the Fantastic Force ATA and pay the points. Like DFitz1138 said, he can then use the Fantastic Force ATA plus another team ability he copied through his wild card team ability.

From the Player's Guide:

Let's say I was playing a Dark Avengers team that had both WOS Bullseye and Monnstone on it.

I want to use the dark avengers ATA, I assign it to bullseye and anyone else who has the keyword.

Now I also want to put thunderbolts on moonstone. ATA's must be assigned to any figure that meets the prerequisites, and this includes bullseye. Bullseye already has an ATA though.

I know any figure can legally only have one ata on them at a time, so what would happen here? Would I have to assign both ata's but only use one? Would I not be able to play thunderbolts at all?

You cannnot play Thunderbolts at all. It's not one ATA per character, it's one ATA per force. So the force you built could only be assigned Thunderbolts or Dark Avengers. It cannot be assigned both ATAs.

From p. 17 of the 2010 Core Rulebook: