Let's say I am running a Spy theme team with Copycat and Black Widow on it. Let's say that my opponent has a 100 point Captain America. I switch Copycat for Captain America.....Now since Captain America is considered as 'Friendly", could I have him merge with Black Widow and make the duo fig?

If this happens, what would happen then if Copycat fails her Shape Change roll and has to come back to my team but Captain America is still in duo form? Would they auto split and how would I choose the clicks they need to be on?

you would lose your duo piece, game effects transfer to replacement pieces when you split or merge.

If the duo got damaged how would I allocate the clicks? Probably have more damage on the figure that goes back to the opponent huh?

I agree with Banereaver. Your opponent would get the duo character when Copycat goes back to your force.

You are unable to replace characters switched with Copycat.

Copycat and the figure she is swapped with are not added to their new teams force only made friendly. Much in the same way that characters under Mind Control do not become part of the force of the Mind Controler. This is critical for both Unique and Prime figures as if becoming friendly to a force you were considered part of a force Mind Control would be an illegal action to take on a Prime if your force already contained a Prime, and similarly with the Unique rule. Both Copycat and Mind Control share near identical wording in this regard:

Copycat's power works more as a pair of long-duration Mind Control's much like possession.
Also having a second look at the difference between Possession and Infiltrate My Enemies it looks like game design flubbed up and forgot a critical line that was present in Deadman's Possession: "opposing to its owner’s force". Oh well I am sure that will get fixed in the Final Word on Copycat.

I can not find this answer anywhere. So the figure you copy becomes friendly like when you Mind Control. What happens if I push the copied figure till they are KO'd? Do I get the points or my opponent? For example if I mind control a character and crit miss or damage a mystic and the mind controlled character gets KO'd because of the result, I would assign victory points to the person me not my opponent.

When you control an Opponent's figure and that figure is KO'd you are awarded the victory points.

The reason for that is the character goes back to being your opponent's before victory points are calculated. So if you switch with an opponent's figure and they KO that figure you would get the Victory points for it not your opponent. HOWEVER, if you are playing in a multiplayer (Battle Royal) game then the person who KO'd the figure would score those points.

Mind control only lets you give that character a free action, then they become opposing. Also, Mind control does not give a token for the action.

Copycat is not Mind Control. He was only using that as an example since Mind Control is one of the closest parallels we have for her power.

Mind Control: Give this character a close or ranged combat action (minimum range value 4) that deals no damage. A successfully hit target becomes friendly to your force. Each target hit may be assigned one action as a free action, immediately after which the target becomes an opposing character again. Deal this character 1 unavoidable damage if the successfully hit targets’ combined point value is 150 points or more.

INFILTRATE MY ENEMIES: Before placing characters in your starting area, you may choose an opposing character that is 100 points or less. Copycat becomes friendly to that character's force and that character becomes friendly to your force. Any game effects assigned to each of them is now assigned to the other. When Copycat fails a roll for Shape Change or uses Regeneration, after actions resolve, this effect ends and any game effects assigned to each of them is now assigned to the other.

I did use MC because MC says the character becomes friendly to your force, THEN you give the free action.

I can see if the wording said "Each target hit may be assigned one action as a free action as IF they were friendly to your force."

As we know this is a wording game and using "as if" would make a huge difference.