Can cyclops combine his improved targeting to shoot out of adjacency OO-> with his sharpshooter ability to shoot opposing characters THROUGH an opposing adjacent character?

Sorry if this is confusing the way I wrote it...

So it would look like this?

Yes, that is perfectly legal.

No, that is not legal. You cannot make ranged combat attacks against non-adjacent characters when adjacent to an opposing. Sharpshooter allows you to target the adjacent with a ranged attack, but not the non-adjacent. You could outwit through your opponents character though.

Cyclops has improved targeting shoot out of adjacency so he can shoot through an opponent adjacent is just fine because he ignores opposing characters for line of fire as part of sharpshooter.

Sharpshooter also lets you ignore opposing characters. It's not just sharpshooter though. There's Improved Targetting involved as well, which lets him make a ranged combat attack while adjacent to an opposing character.

Ah, I forgot that he had that part of improved targeting, I thought he just ignored blocking. Sorry for my incorrect answer.