"Pater Iūliae est Iūlius". Would this be "Julia's father is Julius", or "The father of Julia is Julius"? I feel like it's missing some words to be the latter. Does it matter? How can I tell?
In general, don't focus on every word having an equivalent in the other language. For example, the single word magistrō would generally be translated into multiple words like "to the master". That's just how translation works—focus on translating the overall meaning, not finding an equivalent to each and every word.
In English, we have multiple ways of combining nouns. We can use Y's X, which is the way we inherited from Anglo-Saxon, or we can use X of Y, which we borrowed from French. There are some places where you can use one but not the other, which come down to differences between French and Anglo-Saxon grammar, but for the most part it's a matter of style.
In Classical Latin, on the other hand, there's just one way: the genitive. So whether you translate it with 's or of comes down to what sounds better in context in English. (Sometimes you can also turn a noun into an adjective in Latin, like pater Jūliānus est Jūlius, but this is a lot more restricted than the 's and of in English. When this happens, you'll often end up translating it into 's or of, just like the genitive.)