Q: Can I put the car in reverse gear by using the brake, like in several other games?

A: Yes. Turn on the Automatic Reverse option in Options -> Realism. After braking to a complete stop the car will start to reverse after a short time of continuously stepping on the brake pedal or pressing the appropriate key. (Note that the “automatic gearbox” option must be turned on as well, or the car will not automatically select the reverse gear.)