Why not "Moje auto stojí na vaší ulici"? Don't czech see a street as a surface?
Not always. We say "na ulici" which means "on the street, outside", but when indicating a precise location or address we rather use "v name_or_pronoun ulici".
Just note for advanced, "na ulici" could also mean homeless.
yes, "on the street" can also mean homeless.
Would je also be acceptable instead of stojí? If not, please explain why?
Of course, it is accepted.
So, why it does accept neither "je ve tvoje ulici" nor "je na tvoje ulici"?
locative is "tvojí"
Is prepositional case used here?
There is no such case in Czech, only in Russian, because Russian lost the original locative case.
Does the use of the verb "stojí" indicate in Czech that the car is in the street but not moving? If so, the English to translate from should say "My car is standing in your street".
Why not... MOJE AUTO JE VE TVOJI ULICI?
"Moje auto je ve tvojí ulici" is an accepted answer. You probably had another mistake there. Why don't you use the REPORT BUTTON?