If they are going to include the short vowel signs, it would also be helpful to include the tanwin signs as well. It would be easier to track the definite and indefinite-ness of each word and the type of case each word pertains to.
Well, there are indeed signs for Tanwin and i see them on Duolingo on and off. Anyway, it doesn't matter much, sort of. As long as the noun does not have the definite article (AL) then of course it is indefinite.
The audio is correct actually, but probably you are referring to "why there is no -un sound at the end of Kabeerah" (i.e. on ta-marbuta). This -(v)n sound at the end of words is called Tanwin or Nunation, and it can be considered a marker for indefinite noun (like the example above). Anyway, the last vowel or tanwin in the sentence can be omitted and not pronounced if the word is at the end of the sentence. This is simply a matter of "speech fluency" or how the flow of words work. Since (كبيرة) is at the end of the sentence here, we don't really need to say (kabeeratun). If this word was in the middle of the sentence or at its beginning (and followed by other words) we would have to say it as (kabeeratun) to assist the flow of the words after (kinda filling the gap or the silence between words with Tanwin, sorta). Hope it makes sense!