Firma potrzebuje miliona złotych.

Because the subject is firma and the verb is in the 3rd person singular present tense.

The infinitive is potrzebować = to need.

Present-tense forms:

• ja potrzebuję = I need
• ty potrzebujesz = you need
• on / ona / ono potrzebuje = he / she / it needs
• firma potrzebuje = the company needs

So potrzebuje matches firma just like needs matches the company in English.

In the present tense, Polish verbs usually do not show gender.

So:

• kobieta potrzebuje = the woman needs
• mężczyzna potrzebuje = the man needs
• dziecko potrzebuje = the child needs
• firma potrzebuje = the company needs

The form potrzebuje stays the same for all 3rd-person singular subjects.

Gender becomes more visible in places like the past tense:

• firma potrzebowała
• bank potrzebował

Because potrzebować normally takes its object in the genitive case in standard Polish.

So the basic form:

• milion = million

changes here to the genitive:

• miliona

Compare:

• Mam milion złotych. = I have a million zlotys.
• Potrzebuję miliona złotych. = I need a million zlotys.

The change from milion to miliona is caused by the verb potrzebować.

Because after amount words like milion, the counted noun normally goes into the genitive plural.

So:

• milion złotych = a million zlotys

Here the whole phrase is inside a structure required by potrzebować, so:

• milion becomes miliona
• złotych stays genitive plural

That gives:

• miliona złotych

This is very common with money:

• jeden złoty
• dwa złote
• pięć złotych
• milion złotych

In standard Polish, yes: when potrzebować takes a noun object, that object is normally in the genitive.

Examples:

• potrzebuję czasu = I need time
• potrzebujesz pomocy = you need help
• firma potrzebuje pieniędzy = the company needs money
• firma potrzebuje miliona złotych = the company needs a million zlotys

So for learners, the safest rule is:

potrzebować + genitive

Very much so, yes. Words like milion, miliard, and tysiąc behave a lot like nouns.

That is why they can decline:

• milion
• miliona
• milionowi, etc.

And that is also why the noun after them is usually in the genitive plural:

• milion ludzi = a million people
• milion dolarów = a million dollars
• milion złotych = a million zlotys

So in miliona złotych, you are seeing:

• miliona = declined form of milion
• złotych = genitive plural after an amount word

Because Polish does not have articles like English a / an / the.

So firma can mean:

• a company
• the company

The exact meaning depends on context.

In an isolated sentence, English may translate it either way depending on what sounds most natural:

• The company needs a million zlotys
• A company needs a million zlotys

Yes. Polish word order is more flexible than English word order.

The neutral order here is:

• Firma potrzebuje miliona złotych.

That is a normal subject + verb + object sentence.

But you can change the order for emphasis or style:

• Miliona złotych potrzebuje firma.
• Potrzebuje firma miliona złotych.

These alternatives are possible, but they sound more marked. For a learner, Firma potrzebuje miliona złotych is the safest, most neutral version.

Not in standard Polish.

Because potrzebować requires the genitive, you cannot use plain jeden milion here.

You would need:

• Firma potrzebuje jednego miliona złotych.

But in most situations, Polish simply says:

• Firma potrzebuje miliona złotych.

Using jednego adds emphasis, something like exactly one million or one full million.

So:

• miliona złotych = the normal way
• jednego miliona złotych = more emphatic

A rough pronunciation guide:

Firma potrzebuje miliona złotych
≈ FIR-ma po-tshe-BU-yeh mee-LYO-na ZWO-tikh

A few useful sound notes:

• rz in potrzebuje sounds like Polish ż; roughly like the s in measure, but harder
• j sounds like English y
• ł in złotych sounds like English w
• ch sounds like a rough h/kh
• y in złotych is not exactly an English sound; it is a short central vowel

Stress in Polish is usually on the second-to-last syllable:

• fir-MA? No — actually FIR-ma because it has only two syllables
• po-trze-BU-je
• mi-LIO-na
• ZŁO-tych

It can mean either, depending on context.

Potrzebuje is present tense, so it can express:

• a current need: The company needs a million zlotys right now
• a general situation: The company needs a million zlotys (in order to continue / for the project / as a requirement)

Polish often leaves that distinction to context, just as English does with needs.

Firma is in the nominative case, because it is the subject of the sentence.

Basic structure:

• Firma = subject, nominative
• potrzebuje = verb
• miliona złotych = object phrase governed by potrzebować, so genitive

So the sentence is a good example of:

• nominative subject
• genitive object

That combination is very common with potrzebować.