('bint' is 'girl' rather than 'woman')
That said, this is simply a matter of adjective order which differs in usage between languages (like in English it is quantity-quality/value-size-temperature-age-shape-color-Proper (nationality/etc.)-material-purpose. You would say I have 'few charming old round Victorian silvers' not I have 'Victorian round charming old few silvers'). It is just a matter of traditional usage.
'Arab American people' as a phrase in English is understood generally to mean Americans of Arab origins (without getting much into identity definitions), where they themselves choose to identify themselves in this word order.
The equivalent of that, in meaning, in Arabic is 'American-Arab people'
So the transliteration of this sentence is 'an American Arab girl' The translation of meaning is 'an Arab American girl'
I think you're correct that's it should be American-Arab woman. When translating from Arabic to English and vice versa, the distance the adjective is from the noun should remain the same (closest adjective to noun should remain the closest adjective to the noun in both languages. So the closest adjective to the noun بنت / girl is عربية / Arab.
So بنت عربية أمريكية should be American-Arab girl.
I started by learning the alphabet on its own (isolated letters) and how they sound on their own first. So I spent a few days learning that on my own before jumping on Duolingo. I feel like that helped me a lot understanding what I'm learning here, I barely have to guess because I know the basis of it I feel and always come back to it.
It's a pity for me, but I will have to stop this Arabic Course. There never has been offered the new vocabulary translated in words or pictures like Duolingo does in the French and English lessions. There I really appreciate these ways of presentation those learning lessions. Here in this course I miss it very much from the beginning. Not to mention, that English is not my native language. But the Arabic language is anyway difficult enough to learn for me, and also very often is to small to read. And now all this guessing of the meaning of new words and also there isn't at all explained all new presented grammar with all this new endings of un and tun and sometimes these are written but not spoken. Pity that. What's the use to have to look up everything of it in other webpages? Therefore.... Good bye, Dear other learners. But I liked to learn the arabic alphabet and found this approach to learning it very well. But even there sometimes I had the feeling that some of the offered little alphabet words have had a meaning, but didn't look them up. Good by then. May be, I do still some alphabet and ignore all the sentences, until I am through with the alphabet.
If you are using the web version of duo you can hover over the words to get the meanings. If you are using the android then you are out of luck. I don't love this course but it isn't unusable. I would have preferred that they present vocabulary and more of it from the beginning. I truly hate traditional language courses in that they always begin with the standard presentation of greetings. Usually duolingo courses begin with other vocabulary and simple sentences aside from greetings which allows me to jump into speaking about a wider variety of topics when I travel. If I wanted just an intro to greetings I could pick that up in any tourist guidebook. I agree that the alphabet words given should have all had a meaning and should have had the meaning presented upon the question being answered so that those of us who want to could begin acquiring an arabic vocabulary bank. Those words could have been used in subsequent lessons. This course is far too much like a traditional language course in too many ways that I don't like.
Not sure what DUO was thinking when they released this course. It is put together at an amateur level at best. The hover over hints are toss up and I have found myself just guessing more than any other language on here. Like you Martina I am here just out of curiosity but good lord this is almost a joke. I'm trying here but they should put this back in the incubator and rethink this course, even after four levels you might be better off using google translate. A regular cold chicken umm …..sure.