where is the -un in the audio coming from? Is it the nominative case? and if so when do I use it?
Yes, it's the nominative indefinite ending. In formal MSA (and Qurani Arabic), you have three cases and six endings:
Nominative: -u (definite) / -un (indefinite)
Accusative: -a (definite) / -an (indefinite)
Genitive: -i (definite) / -in (indefinite)
The nominative is used as you'd expect – for the subject of the sentence.
تَكَلَّمَ رَجُلٌ لَطيفٌ مَعِي أَمسِ
takallama rajulun latifun ma3i amsi
"A nice man spoke to me yesterday"
يُعجِبنا البَيتُ الجَديدُ
yu3jibna l-baytu l-jadidu
"We like the new house" ("The new house pleases us")
The accusative is also used as you'd expect – for the direct object of the verb. Note that a final alif will always be added for the accusative indefinite ending (except after a ta' marbuta).
هَل اِشتَرَيتَ هاتِفاً غاليّاً؟
hal ištarayta hatifan ghaliyyan?
"Did you buy an expensive phone?"
"I love reading"
The genitive is used both on the possessor in an idafah construct (idafah being the genitive construct in Arabic), and on nouns following prepositions.
"The capital of Egypt"
(Note that the definite genitive ending is used, not the indefinite, even though there is no definite article on the noun. This is due to idafah, but I won't go into detail on that here)
رَأَيتُهُ في كِتابٍ قَديمٍ
ra'aytuhu fi kitabin qadimin
"I saw it in an old book"
المَفاتِحُ عَلى الطاوِلةِ
al-mafati7u 3ala T-Tawilati
"The keys are on the table"
Note that in more casual MSA, the endings aren't used as much. For example, the last sentence, "المفاتح على الطاولة", would be more commonly pronounced "al-mafati7 3ala T-Tawila". Also in casual MSA, at the end of the sentence, the ending isn't used; this can be seen in the Duolingo exercise; "baytun kabir", not "baytun kabirun" (which would be the official formal pronunciation). Furthermore, the cases disappear completely in the dialects.
إذا كان في النص أي خطأ فاعلنني من فضلك.
A year or two ago, I could right click my mouse and ask the computer to translate sentences. Do you know if Duolingo took this feature away from us or if it is a Windows 10 change? It was a great feature!
Is it possible to add transcription please? I can understand a little bit of what she's saying, but it's still a new language and a new alphabet for me. With transcription it'd be much easier for me
Believe me, having transcription would only make it harder for you to actually learn to read. One should completely hop on the new writing system asap, otherwise you'll keep peeking at the latin letters instead of getting comfortable with the new ones. Best regards.
You was right. After a few days of trying to read without transcription I finally got it. At first I tried to remember the letters with small stories, like "this is a egyptian eye جand that's a snake ى and this one looks like emoji ت" But know I recognize some of that very quick without these stories. So yeah. That's better without transcription
Where is the -un in the spelling? Should it be reflected in the spelling if it is pronounced?
It is because of the nominative ending -un, since the object is indefinite. Check out linguafiqari's answer above!
But if you are, like me, worried because there is no 'n' ن, it's due to something called 'nunation'. There is a good article on wikipedia about this, but basically is a word ending in an alveolar nasal without adding the letter 'nun' ن .