Functionally, only the third option is really correct. It sounds quite odd to say 'the engine drives the car' since in most cases a human drives it, although as your third sentence indicates, the car needs an engine to work. The first sentence is in the passive voice, whilst the second is in the active voice.

They're all correct, just be aware that, when you talk about 'driving' and 'cars', the regular person will first think of 'operating and controlling'. Only the engineer will first think of 'propelling by force'. The word has these two different meanings when it comes to cars. However in your examples it should be obvious what is meant. If in doubt, say 'drives forward' or 'propels'.

Because of the ambiguity, it would be better to say "the engine powers the car." However, the transmission and other components that transmit power from the engine to the wheels is called the "drivetrain."

both are acceptable