Translation:Where is Rosa?
For starters, you might know by now that we don't usually write the harakat or short vowels when we write - so the fatHa on (N) in (ayna) here is not written, and that's OK (though I'd expect Duolingo to put it there as a guide for new comers).
Now, the word itself, is actually (ayna). This is the original form. When the word comes alone (any word not just this one), or when a word comes at the end of the sentence, typically the last vowel is dropped. It is added as a form of continuation of speech, and to help with the flow of the speech (and of course there's a grammatical story behind this but it's out of the scope for now). So when a word comes at the end or simply mentioned alone, there is no need to add that last vowel, and (ayna) becomes (ayn).
Now, I can see that they fixed the audio and the machine does say (ayna) instead of (ayn) and this is how it should be because (ayna) is at the beginning of the sentence and followed by another word
for the standards of the standard Arabic, it would be cumbersome to speak and omitting the vowels on the last consonant of every word.
I share BubDuck's puzzlement. If the word is basically ayna, I can't see why Duolingo doesn't give it to us in that form. Especially, as it often comes first in a sentence, as it is more likely than many words to have another word following it, and therefore have the final A pronounced. Do I guess correctly that this rule about dropping the last vowel of the last word in the sentence doesn't apply to all vowels but only if the last vowel is a harakat?
Yes, it is dropped in case of the Harakat. In fact, I'm saying dropped to approximate the idea for learners who are used to Latin alphabet. In essence, in Arabic, we do put Sukún on the letter (which is a vowel-silent marker), or simply leave the consonant without any markers (as we do in every day writing).
As for Duolingo, well, there is a lot needed for this course specifically to raise its level to some acceptance level. I'm a native and I don't see this course is technically out of the Beta stage after one year or more from establishing this course.
Yes, it's mainly the short vowels which are affected at the end of the sentence. Writing them or not well, it's a personal choice, but yeah maybe one can type sukún if they wish to at the end of the word at the end of the sentence - though i think that would be a bit misleading.
in Quran, at the end of each verse or line, even though we don't say out the last short vowel at the end, but it is written because it is important grammatically. Also, those who study Quran recitation might not stop at the conventional end of the sentence or verse and continue to the next one, so the vowel marker should be there anyway. However, this is for Quran which has a literature on its own when it comes to orthography and reading.