Original Wording

In Contact with Cerebro: If Professor X is in your starting area, he can draw lines of fire and count Range for his Speed, Attack, and Damage powers from the square of any friendly character with whom he shares a keyword.

I've Learned Your Secrets: Professor X can use Outwit. Once per turn, when he uses Outwit to counter a standard power, he may immediately use Outwit again, but only to counter a power of the same color.

Errata

In Contact with Cerebro: If Professor X is in your starting area, he can draw lines of fire and count range and squares for his Speed, Attack, and Damage powers from the square of any single friendly character with whom he shares a keyword.

In all of the Q&A below, I refer to "Friendly characters" instead of the more cumbersome "Friendly character that he shares a keyword with". Please don't take any answers below to mean that the keyword requirement is optional.

Can Professor X use powers like Outwit that do not require range but "10 squares" through friendly characters?
Yes - the draft errata adds "and squares" to the power to allow for this.

Can Professor X use one friendly character to determine range and a different character to determine line of fire?
No - the draft errata adds "single" to the power to clarify this.

Can Professor X be within range himself while using another friendly character for line of fire (or, reverse, have line of fire himself to the target and use a friendly character for range)?
No - when Professor X is using In Contact With Cerebro, if he using a character to for line of fire, then he is also using them for range/squares.

Does Professor X need line of fire or range to the friendly character he is using?
No. His teammate can be all the way across the board, behind blocking terrain, and Prof X can till fire through them.

Can Professor X make a ranged combat attack through the squares of the friendly figures?
As long as he is using a Speed, Attack, or Damage power, then yes. But if he is not using such a power then he cannot. For example, if he is on click #5 or 6, he can either attack with Incapacitate through another character or he can use his Outwit special power. He would not be able to make an attack tht damaged the target (barring push damage through Incap).

Which character "counts" when figuring out game effects that are relevant based on adjacency? Things like Enhancement or even whether or not the character can make a ranged attack.
Professor X is the character making the ranged combat attack. The only thing that is different through In Contact With Cerebro is that when one draws a line of fire, instead of drawing that line of fire between Professor X and the target, it can be drawn between Professor X's teammate and the target. Everything else applies normally.

So Professor X would need to be adjacent to a character using Enhancement in order to get the bonus. Professor X would need to be adjacent to a SHIELD team member in order to get the boost to range or damage. Professor X adjacent to an opposing character would prevent him from making a ranged combat attack, not one adjacent to the friendly character. A character using Probability Control would need to draw line of fire to Professor X, not the friendly character.

If Professor X were to choose to use a friendly for his line of fire, would he gain the benefit of the character's ability to ignore characters for line of fire?
No. All Professor X gets to do is use the friendly character's square as his "starting point" for his lines of fire. Everything else is the same as if it were Professor X himself.

Can Professor X use In Contact with Cerebro to draw line of fire and count range with powers he can use, but doesn't possess, such as themed team PC or powers temporarily granted to him by Mikron O' Jeneus?
No. Professor X can only use ICwC with his powers, which are powers that he actually possesses.

Updated Q&A

Updated to reflect PG errata.

Updated Q&A.