Traditional writers advise against using 'there be ...' since 'there' is sort of an empty subject (that is it doesn't mean anything_ just there to fill the subject slot) although in speaking it's very common. 'There be' is used to introduce topics so most of the times it's followed by an indefinite article (like a/an) rather than a definite one (like the). Based on this, the first sentence sounds off a bit since using 'the' before 'car' shows that the car has already been introduced to the listener.
Sentence two is a good substitute for your first sentence.
Sentence three introduces a topic (a car being in a parking lot) and that's it. The next time you need to refer to that car you'll make it specific like saying, '...and that car was my dad's' or you'll use a pronoun like, '...and turned out it was my dad's'
Sentence four puts 'a car' in the subject place which means the rest of the sentence is about 'a car'; that means you intend to draw the listener's attention to it as in,
'Um! Meg! A car is in the parking lot! Do you mind explaining why you said there is no car there?!'