Translation:The big black car is passing by in front of the school.
The use of "by" in the sentence doesn't sound old fashioned to me, it just sounds awkward and redundant. I don't mind Duolingo's awkward English and even prefer it when it better expresses the full meaning of the Hungarian sentence. In this case however, I don't think "by" adds anything.
This car is currently in front of the school, and is moving along in front of the school. (Perhaps we are watching it go by from the window of the school).
Az iskola elé would be useful for something that has moved (or is moving) to a position in front of the school, from somewhere not in front of the school.