1 - If you use an ATA, can you still use your regular TA? Can your Alt TA be copied by wild cards on your team? Can you have multiple ATA's on the same figure if they qualify for each?

2 - If you have a power like shape change or impervious and you are outwitted and then take a click of damage but the power is still there on the next click, is it still outwitted? If so, what about if you have a power outwitted like impervious, take 2 clicks of damage where you lost impervious (say invulnerable came up) and then the dial went back to impervious, would it still be gone?

3 - With a figure with Power Cosmic, can you turn it off and take pushing damage? If so, what if you had a Power Cosmic figure with the Infinity Gauntlet, could you turn off Power Cosmic and the built in willpower from gauntlet to take pushing damage?

4 - When making a TK attack on a stealthed enemy within range, if the enemy has shape change, would they still be allowed to roll shape change even though you don't have to have line of sight to make the TK attack on the target square?

I'm sure there are a few more that I'm not 100% sure on but this is enough for now. Thank you in advance.

In most cases, yes.

In most cases, yes.
You can only play one ATA per team.
Yes.

Yes.

THe willpower granted by Power Cosmic/Quintessance and the Gauntlet are optional. You may turn them off to take pushing damage.

Yes.

Willpower is not optional. Ignoring pushing damage is optional, if you have (or "can use") Willpower.

My wording/phrasing was off, the intent was the same. Six of one, half-dozen of the other.

Not really. The result is the same, but how you get there isn't. It may seem like picking nits, but it's important for people to realize that powers are not optional. They may provide a choice on using the effect, but the power itself cannot be turned off. So while the specific answer ("yes") is correct, the explanation is potentially misleading. The devil is in the details.