Why is "is there a car or a girl?" not right? Am I not catching up something here?
First, it needs to be "the car" and "the girl" (definite article, not indefinite).
Second, the word "there" in this sentence is describing location. If you say "Is there a car?" you're basically asking, "Does a car exist?" You need to phrase it as, "Is the car there?" in order to make it clear that you're asking about a certain location.