Should I give my main character a girlfriend?

Nah. Maybe an infatuation, maybe he thinks he's "in love" with someone, but based on his personality I think he'd be irritated and tense around a girlfriend. Have him pursue someone as a side-plot. I liked him a little, but Zach would be far more likeable if he had a trait that made us want him to succeed. Honesty, a want for good, loyalty, determination, will to succeed, affectionate side, etc. Good luck :)