Extra cars:
Start a new race. Choose the "Begin Career" selection. Enter GO_BEARS! (for stock cars) or GO_BRUINS! (for formula one cars) at the "Register" screen. Note: "_" indicates a space.

In-race car modifications:
Pause the game during a race. Enter the "Race Statistics" screen. Hold Circle and press X. A car editor menu with the following options will appear:

Drafting effect
Draft distance
Front downforce
Rear downforce
Fuel consumption rate
Incremental braking
Tire wear rate
AI speed percentage (50-150)
Torque spins
Centrifugal force

Note that some of these options can be set with a negative number.