What does a shot or attempted shot have to hit prior to being touched again by the shooter? Can you shoot it off the backboard to yourself? Is there a differnce between college and high school?

A shot attempt doesn't need to hit anything for the player to have the ability to recover it and have a new dribble to use. Only in the NBA is there a restriction on this.

The only requirement is that the official believes that the "shot" was indeed intended to be a "shot". Once that decision is made any player can pick up the ball since both team and player control has ended.