Lipiec jest miesiącem roku could mean both , but Lipiec jest miesiącem w roku means July is a month of the year , and with your sentence , ( 1 ) Ten miesiąc jest lipcem or ( 2 ) Ten miesiąc to lipiec ( better ) or eventually ( 3 ) Ten miesiąc nazywa się lipiec ( That month is named "Lipiec" )
How does the Genitive case work here? I can follow the template of "<Nom> jest <Inst>", but I don't have a matching one that includes a Genitive. Is the year belonging to the month, or the month belonging to the year? (I'm taking YuvalRudni's comment below to mean the latter.)
Does this template work in general, so "pies jest zwierzęciem człowieka" would translate to "A dog is a man's animal"? Is there a piece of the course that I can skip ahead to (or wait for) that offers a deeper explanation of how the grammar works here instead?
In general noun+noun(genitive) indicated possesion/belonging, with the noun in genitive = owner.
Unfortunately we don't have many explanations in the course, and possession is rather easy thing. There is a very long guide about genitive, and has one sentence about possesion
2.To describe ownership
When used with a noun:
"koszula(nom.) ojca (gen.)" - [the shirt of the father] But when the ownership is expressed with a pronoun, the case of pronoun has to be >the same as case of possessed noun:
"moja(nom.) koszula(nom.)" - [my shirt] "nie ma mojej(gen.) koszuli(gen.)" - [there is not my shirt] - Genitive because of >negation ("nie ma" is a verb-like construction), not because of ownership.
It is used to describe a part of something:
"kawałek(nom.) chleba (gen.)" - [a piece of bread] "odcinek(nom.) serialu (gen.)" - [an episode of tv-series]