This translation is correct: "Their auto stood across from our house." "auto" and "car" are the same.
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.