Car is outside. -> The car is outside.

I think both:
"The car is outside."
and
"A car is outside."

are valid choices. "There is a car outside." would require an extra word "є" somewhere.

I think that article "the" or "a" at the beginning of a sentence can be omitted in this case.

"There is a car outside." would require an extra word "Там авто на драже". "ТамĆ means "There".

"There is a car outside." - be careful not to confuse "there" with "there is". "Там" means "There" (as in the adverb), however "there is" is simply an existence copula (not implying any direction), as in Russian "есть" or Ukrainian/Rusyn "є". That is why we can have the sentence "There is a car here." in English.

In Slavic languages, of course, no article is necessary. However, in English, you MUST choose an article.
I'll call some native English speakers to discuss.
@AlanF_US @patgfisher @blay_paul @jaxhere @CarpeLanam @Airvian @Hybrid

I'm sorry for stepping in but I also wonder if "на драже" (which literally means on the road) can be translated as outside.

Yes, "на драже" can be interpreted as "outside". For example "Орех на драже" means "Walnut is outside", on the street, not "on the road".

OK, then we have two sentences for "Авто на драже."
One is "The car is outside" i.e. My (your, their etc.) car is outside.
Second would be "A car is outside" i.e. One (any, somebody's etc.) car is outside).
If I am wrong, please let me know.

I agree with cueyayotl.
Why can't it be "There is a car outside."? I think it sounds more typical for English. If you want to say "Там авто на драже" it would be "There is a car outside over there" or something.

"There is a car outside" would be in Rusyn "Там авто на драже", or "Єст авто на драже", or "Там єден авто на драже", or "Єст єден авто на драже".

What's the difference in the meaning between "There is a car outside" and "A car is outside"?

Basically, the meaning of both sentences is the same, although "There is a car outside" is more assertive, sounds like a warning. This is how I feel it.

Yes, agree, there is only a subtle difference when speaker says that. They can be used interchangeably.

I see, thank both of you for the explanation.