You can study without learning, and you can learn without studying. They're related, but not synonymous.
She studied for her law exam all night, but she couldn't remember anything in class the next day. She learned nothing.
The flooded bathroom made me learn my lesson: Close the shower doors before turning on the water. No studying required.
Do know why it does not translate to Corinna Learns Latin Language.
If a singular noun is feminine, its plural is feminine.
If a singular noun is masculine, its plural is masculine.
If a singular noun is neuter, its plural is neuter.
And of course there are the different declensions.
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.
I got the answer correct merely because I could recognize the words. But I'm still confused over the logic in Latin syntax. If I were to write from English to Latin without the scrambled words as an aide, I would not get full points.
Someone knows a decent online book or a source to better understand Latin syntax? Much appreciated.
Language has no logic, only convention. I'm sure others can point you to good resources, but in a nutshell:
Latin syntax is a little bit more flexible than English's is, but broadly, it defaults this way:
Basic sentence structure is Subject-Object-Verb.
Adjectives generally come after nouns, except for determiners and numbers. Similar grammar has survived in the Romance languages.
Adverbs always come before verbs, although they don't have to be side-by-side.
The conjugated verb comes last. It's a bit backwards of English. We say "I want to sleep", Latin says "Dormire volo". This is how tense endings evolved in the Romance languages.
You can hardly be said to know a language without discovering a few of its names. The whole point of language learning is to embrace the currently unfamiliar gibberish.
Plus, there are no universally obvious names. Even your example of Livia was new to me. Within English alone, the phrase "Tom, Dick and Harry" expresses the common public in Britain but someone named Dick is of much amusement to many Americans.