You don't HAVE to have an article here in english when it is not part of a sentence.
Well... if it was just one noun phrase (dziewczynka) we would definitely accept it without an article. here... I'm not so sure, but ok, it's not a sentence, after all. Will be allowed now.
If they're being used in a sentence, generally yes. But just standing by themselves (as they are here), not necessarily.
Shouldn't Dziewczyna be valid here too? Both mean girl, one just isn't diminutive.
'The girl and a boy' was my only correct option... So the noun in its own can be definite or indefinite?
The main answer is "a girl and a boy", but all variants seem acceptable. As Polish doesn't use articles, in most sentences (and this is just a phrase, so even less context) both versions would be correct.