"She studies in New York."
Translation:Ea Novi Eboraci studet.
I was confused about this initially, but this stackexchang cleared it up: https://latin.stackexchange.com/questions/280/why-does-the-ablative-case-also-include-the-locative#285 The locative case was eventually merged into the ablative.
The case is different, the case being the use/function in the sentence.
Here, Novi Eboraci is the locative case, specifying where something happens or is located. Her studying takes place in New York. Note, however, that the locative is only available for cities, towns, small islands, and a few other nouns (such as domus). Novi Eboraci can also be the genitive form.
Novum Eboracum is the nominative, accusative, and vocative form.
The nominative would be used if New York was the subject of the sentence, like in the sentence: New York has streets. -> Novum Eboracum vias habet.
The accusative would usually be used as the direct object, like in the sentence: I love New York. -> Novum Eboracum amo.
The vocative is used for direct address, like in: Hello New York! -> Ave Novum Eboracum!
Novi can be the genitive case as well as the locative. The locative will look the same as the genitive for nouns in the first and second declension (Novum Eboracum being second declension). The overlap in endings can sometimes make sentences ambiguous in there intended meaning but often context solves this issue.
The locative specifies a location, where something is, occurs, etc. That is why it makes sense to be the locative here, she studies in New York. Not all words have this case.
The genitive is most often used to express some relationship between the noun in the genitive and the noun it modifies, such as possession, material, etc. It acts much like an adjective.
So how would you write "He is the mayor of New York" and "He is the mayor in New York". Based on what you said, I assume the former would be genitive and the latter locative and I also assume the sentences would look the same because the locative and the genitive look the same.
Is/Ea/Id is the third person pronoun (he/she/it) and was used sparingly since the verb conveys the subject. These were saved for emphasis or making clear the subject. This isn't a hard rule, but a good default.
Ille/Illa/Illud are demonstratives. Consider translating as "That" so "Illa puella" is "that girl." It can also be used to convey a connotation of fame. Which Caesar? THAT Caesar.
Illa, depending of the sentences, can be "that" (feminine that) or "she".
Illa when placed in a sentence without a noun to modify (that girl), is always the "she". (SHE sleeps here, we can't use a "that").
I think there's an ambiguity when you have some sentences like, "Est puella illa/Illa est puella", as there's a noun to modify like a "that" and a verb for being its pronoun-subject.
Could someone confirm that it is "that" in this sentence? I'm not sure.
To ask it clearly "Est puella illa/Illa est puella" would be rather She is the/a girl, or She is that girl?