Translation:Their car stood across from our house.
What is the meaning of stand in this sentence? Is it only included literally in the English translation for the sake of clarity?
The meaning is basically the same as "was", but it is included to better demonstrate the Czech word "stálo".
There had been five of them in a car, but now the car stood empty near the ruins in the Frye yard.
This translation is correct: "Their auto stood across from our house." "auto" and "car" are the same.
They are but Duolingo recommends only to accept most common synonyms and CAR is roughly 10x more common than AUTO in written English (Ngrams), so it's probably even more in spoken English.
BTW: Do you use that word when you speak? :) (I'm genuinely curious.)