I was under the impression that Quirrell was being possessed by the other 2/7 of Voldemort's soul that had not at that time been bound into horcruces, and was just wandering around the earth.

The diary is proof of Voldemort being Slytherin's heir, the snake is a compromise measure so that he could get a sixth horcrux--it was only created as one recently, during book 4.

If Harry (or his scar) is both the fifth horcrux and the intended victim for creating the fifth horcrux, that's kind of weird... maybe it was intended that he be turned into an inferius or something?