1. Shawn decided to pretend to be a psychic because as one of his ploys to get back at his father, he uses his amazing powers of observation to call tips in to the police department. One such tip was so accurate that the police put him high up on the suspect list. To save himself from jail time, he convinced the police that his accuracy came from psychic insight.
2. Dule Hill's Gus is -- perhaps a tongue-in-cheek homage to reality tv -- a pharmaceutical sales rep.
3. Corbin Berson's character is a retired, highly repsected, police detective who was determined that his son would follow in his footsteps. He's also a perfectionist and has a problem with his son's more laid-back approach to life. He did manage to train Shawn's powers of observation, but alienated him in the process. He's grumpy because a) Shawn did not become a police detective, and 2) he feels Shawn is wasting his considerable talents.
You'll see a lot of this background exposition, in a highly entertaining fashion, if you ever do get to see the pilot.