Varus is implied to be ambidextrous, as evidenced by having two skin arts that have him holding his bow in his left hand and the other two having it in his right.
However, Varus is most likely right eye dominant, since archers traditionally wield their bow according to their eye-dominance rather than their hand-dominance, due to the fact that he only holds his bow in his left hand in-game.
His namesake might be the infamous Roman general Publius Quinctilius Varus, who foolishly led three Roman legions to their demise during the Battle of Teutoburg Forest. While League of Legends's Varus defends his charge but loses everything to the Noxian invaders, to which he vows revenge.
Varus is in a state of transformation. He made a decision to sacrifice his humanity (in fact his very self) to gain the means to achieve revenge. The pants are the manifestation of the corruption overtaking him. He only has so much time before it will overtake him.
His pale appearance is of a man whose life is slipping away or being drained. As far as his face, you could find people with many different appearances in all the respective regions of Valoran.
The Owl insignia on his chest has been passed down through generations of "watchers".
The League of Legends art team worked with Gabe and Tycho from Penny Arcade to make a "special edition" champion sneak peek for Varus.
Riot wanted to deliver some of the creepy, fluid feeling of the corruption, it was important to give Varus a forceful, solid, strong weapon that you could identify him with instead of feeling like (as you do for instance with the T1000 from Terminator 2) the bow was just one piece of a big bag of tricks. Also, the visual impact of his animations with a sturdy bow was extremely satisfying.