Fog option:
     Press R2, R1, X, Square, Square, Circle at the cheat menu.

Hidden Cars:
     At  the  "Select Driver" screen press L1 and three news cars will
be selectable.

Hidden Drivers:
     At  the "Select Driver" screen press R1 and five new drivers will
be selectable.

Big head mode option:
     Press Triangle, Square, Square, L2, L1, R2 at the cheat menu.

Unlock Driving 101 FMV sequence:
     Complete all Driving 101 options.

Unlock stuff..

To unlock cheat option: ...and track:    ...you have to: 
Infinite continues                       Complete season mode 
Jump option                              Complete last man standing 
Thick fog               New York         Complete demolition on all
                                         three difficilties 
Rocket wheels           Boston Big Dig   Complete block your opponent on
                                         all three difficilties 
No time out             Moon             Complete time trial on
                                         all three difficilties 
Night drive             Alpine Raceway   Complete lock-on on
                                         all three difficilties 
Death car               Miami            Complete simulation mode