Can I assume that this ability gives the first player the first choice?

For example, suppose that I am playing Copycat and Tellus. My opponent is playing Copycat and Brother Voodoo.

My opponent wants to steal my Tellus. But, if I'm the first player, do I get to do the following:

(a) I use my Copycat to copy my opponent's Copycat. (That is, I give my opponent my Copycat and take his Copycat.)
(b) Now, I have a second "Infiltrate My Enemies" ability to use (the one from my opponent's Copycat which hasn't been used yet). So, now I use that ability to copy Brother Voodoo (that is, I give my opponent my Copycat and take his Brother Voodoo).

So, now I have Brother Voodoo and Tellus. My opponent has Copycat and Copycat. And both the Copycats have used their "Infiltrate" abilities, so my opponent's stuck with both Copycats.

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Or would it be a more simultaneous sort of thing:

I copy my opponent's Copycat who copies my Tellus at the same time.

But, wait, that couldn't work because my opponent couldn't then give me his Copycat if I've already taken it.

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Also, how does this work with other game effects happening at the same time?

For example, I have Copycat and a full Infinity Gauntlet. My opponent has Lydea Mallor and a full Book of the Skull.

I go first. My opponent wants to use Lydea to take the Soul Gem off of my Infinty Gauntlet.

Instead, does this happen?:

I use Copycat to switch with Lydea. Now, I have Lydea, so I take Angrir's Hammer off of my opponent's Book and give it to Lydea.

(And, yes, more Copycat threads coming, once I figure out how to break the game with two of the same unique on my team. Having two Agent Coulsons is cool, but doesn't break the rules.)

Also, how does Copycat interact with Victoria Hand?

TRAITOR, OR NOT?: Give Victoria Hand a power action if she began the game on your force. She becomes friendly to an opponent's force. At the beginning of each of that opponent's turns, that player deals 1 unavoidable damage to another character friendly to Victoria Hand.

If I use Copycat to steal my opponent's Victoria Hand, did Victoria begin the game on my force or on my opponent's force?

I think that is the way it works, certainly if you are playing Copycat and come across an opponent also playing Copycat you really really want to win that dice roll otherwise you will end up with two of them. So playing Copycat in a themed team or playing her with other figures that can't be affected by her trait is preferable.

Lastly you are trying to break the game playing 2 uniques, surely you should be trying to break the game with 2 primes?

If you swap Copycat for Vicky then she 'began the game on your force', so you can activate her Traitor power.

OK this hurts my brain, what happens in the following example:

Player A has a team
Copycat A
Thor A (doesn't matter what just 100pts)

Player B
Copycat B
Thor B (again 100pt)

Player A wins roll and swaps copycat A with copycat B, they then use copycat B to swap with Thor B.

Players A's team is now Thor A and Thor B and Player B's team is now Copycat A and Copycat B.

Now one of the Thor's attacks copycat A and she fails her shape change roll..

What happens next?

EDIT - I was wrong, nothing to see here.

Another weird interaction

Player A
Copycat A1
Copycat A2

Player B
Thor B1
Thor B2

Copycat A1 swaps with Thor B1 and then Copycat A2 swaps with Copycat A1

So player A team is

Thor B1
Copycat A1

Player B team is

Thor B2
Copycat A2

Edited: Because I got confused with the numbering!

Not sure if you can break the game doing this but I am sure someone is going to try. Watch list anyone?

Actually if Copycat A's effect ends, she would no longer be friendly to player B, so player A would have Copycat A, Thor A, and Thor B while player B only has Copycat B.

I'm assuming that Copycat B1 is the same as Copycat A2 since you renamed them. But if Copycat A2 fails her shape change roll, then her effect would end and she would go back to Player A's team and Copycat A1 would go back to Player B's team since she was friendly to player B before Copycat A2's effect changed that. Copycat A1's effect is still in effect, so she returns to being friendly to Player B.

Sorry it is confusing, will edit the post

Whoa - yeah, this is correct.

I have emailed the rules team just to double check these interactions will let you know what they say. Seems like it could get very messy.

Is Copycat unique?

If the answer is yes, then no shenanigans will allow you to have two Copycat's in your (or your opponents) force. If any kind of swapping would cause this to happen, then that swap can't happen.

The primes under 100 points don't seem to have anything that's breaks the game. I mean, two Brother Voodoos is crazy good, but doesn't break the game. The closest I can see is two The Professors who while adjacent to each other can't be targeted ever, which would be annoying, but not that big a deal.

The rule you're thinking of governs building teams, not gameplay once the battle begins.