New car:
Finish the game and become World Grand Prix Champion, then save the game to a control pack and restart. When the game says "please wait while loading" press and hold the A and B buttons, then go select your car and you'll see a new car.

Engine Select:
Beat the game and save it as World Grand Prix Champion. Now restart the game and highlight a driver at the driver selecting screen, and press Left-C or Right C to change the engine.

Infinite Fuel:
Go to the settings menu and set the fuel to 10%. Although the gauge flashes, you'll never run out!

Thanks to Revolution readers M.J. Farrel, David Ng, Mike the Gamer and Steven Layfield!