"Corinna does not sleep at home."
Translation:Corinna domi non dormit.
I can't go into detail because I'm still learning myself, but apparently "non" specifically negates the verb and therefore does not have to be adjacent to it. Nouns get their own negation, which (assuming they typed it right and I'm remembering it right) is "nella", and the specific form might vary depending on the gender/declension system of the noun.
I think this needs to be stressed in the notes. These sentences in English could go either way 'not at home' 'not sleeping' 'not in the city' 'not studying'. Are Livia and Corinna party animals or is Corinna an insomniac and Livia suffering under lock down and unable to go to Uni?
Because "domi" is in the locative case and does not take any preposition.
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
Latin is Subject-Object-Verb at the top level. Adjectives generally come after nouns, although it's not wrong to put them before. Adverbs come before verbs.
So the first word must be "Corinna" and the last word must be "dormit". In the middle, "non" and "domi" are flexible because even though "domi" is the locative form of the noun "domus", it's functioning adverbially to say where she is sleeping.
It's just different from what you're used to.
Latin is typically subject-object-verb. Adjectives generally go after nouns, adverbs and adverbial phrases generally go before verbs.
The names of cities, towns, and small islands, along with a handful of common nouns such as "domus" and "rus" have a case called "locative", which means you don't use the preposition "in" with them.
Corinna domi non dormit.