is it possible to say "The car was driving away" or can I use the word "drive" only with persons, e.g. "The man was driving away with his car"?
That's a good question.

Certainly the answer is "yes" in usage, but I think (and I'm only guessing here), officially, you're supposed to say "The car was being driven away".

Sometimes people tweak the rule for convenience sakeEmotion: smile. But there is a rule about using active to mean the passive.

eg. The car needs repairing. ( to be repaired )