Learn Polish: Czy tam jest nowy projekt firmy? - Is the company's new project there?

Firmy is the Genitive form of the feminine noun firma (company). In Polish, to show possession (like 'the company's' or 'of the company'), you put the owner in the Genitive case. For most feminine nouns ending in -a, the ending changes to -y.

Why does firmy come after nowy projekt?

In Polish, the owner (in the Genitive case) almost always comes after the thing being owned. So, 'the company's new project' translates literally as 'new project of the company' (nowy projekt firmy).

Why are nowy and projekt in the Nominative case here, rather than Genitive?

Only the owner (firmy) goes into the Genitive case. The thing being owned (nowy projekt) is the main subject of the sentence ('The new project is there'). Subjects always take the default dictionary form, which is the Nominative case.

Does czy mean 'is' in this sentence?

No, czy is just a starter word used to create a yes/no question. The actual word for 'is' here is jest. You can think of czy as a spoken question mark at the beginning of the sentence.