If four people are adjacent to one another can two of them who are diagonal still close combat attack one another and use Outwit/Prob Control on one another?

Example:

12
34

2 and 3 try to attack one another.

Sure. Characters are not terrain, so they don't block on the diagonal for close combat attacks, but they do for ranged combat attacks.

And nope on the Outwit/PC since they require LOF and it'd cross the diagonal which is blocked.

Edi: Not fast enough.

How about Sharpshooters?

Sharpshooter
This character can make ranged combat attacks against adjacent opposing characters. When this character makes a ranged combat attack, it can ignore the effects of opposing characters on line of fire.

PC and Outwit are not ranged combat attacks.

Let's say that 2 is a sharpshooter. If either 1 or 4 is an opposing character to 2 he can draw LoF to 3 when making a ranged combat attack. 2 still couldn't use Outwit, Perplex or Prob (or any other non-attack power that requires LoF) on 3.

Depends.

While characters using the Sharpshooter ability can make ranged combat attacks against adjacent opposing characters, they still require a LOF for those ranged combat attacks. Normally that LOF would be blocked. However, if either 1 or 4 was opposing to the attacker, then the Sharpshooter ability would allow the attacker to ignore that opposing character for purposes of LOF while making the ranged combat attack. In that case, there would be a LOF. (Assuming something else doesn't block the LOF like Stealth.) The character could still not use Perplex, etc. on the diagonally adjacent character because the opposing characters are only ignored when the character using the Sharpshooter ability is making a ranged combat attack. Perplex, etc. is not a ranged combat attack.

I have another question about sharpshooters.
In the situation

1 2 `
3 ` `
` ` 4

1 is a sharpshooter
2, 3 & 4 are opposing to 1
2 & 3 are adjacent to 1
(` are clear terrain)

Now seeing though 1 is a sharpshooter, can he draw a LOF to 4 even though 2 and 3 are adjacent?

No. The sharpshooter ability allows him to make ranged attacks against adjacent opposing characters, but doesn't give him the ability to attack anyone other than adjacent opposing characters while based by an opposing character.

He cannot.

He can only ignore opposing figure for LoF while making a ranged attack. As he is adjacent to 2 and 3, he cannot attack 4.

(I suppose that you could say he can draw the LoF to 4 while making a ranged attack against 2 or 3, but he can't do anything with it.)