auto-mobile/vehicle vs car - All three terms are used in the US and Canada from my experience.

gas vs petrol - "gas" is colloquial IMO, and simply an abbreviation for "gasoline" - but yes, no one uses "petrol" here unless they're a british ex-pat.

gas pedal vs accelerator - both are used. accelerator is more "correct." Some people in the US however don't know the difference between the accelerator and the brake (example: Audi and Toyota "sudden acceleration" scares)

parking brake vs hand brake - both/either are used commonly. As well as "emergency brake," which in many cars, is what it actually is. Some cars have a (locking) foot-operated brake device that is a "parking brake."