Samochód dobrze hamuje.

Samochód is in the nominative singular because it is the subject of the sentence — the thing doing the action.

• samochód = car
• nominative singular masculine inanimate

In this sentence, the car is the thing that brakes well.

Hamuje is the 3rd person singular present tense form of the verb hamować.

So:

• hamować = to brake
• hamuję = I brake / am braking
• hamujesz = you brake
• hamuje = he/she/it brakes

Here it matches samochód, which is singular, so we use hamuje.

Because dobrze is an adverb, and it modifies the verb hamuje.

• dobry = good (adjective, describes a noun)
• dobrze = well (adverb, describes an action)

So:

• dobry samochód = a good car
• samochód dobrze hamuje = the car brakes well

English does the same distinction: good vs well.

It can technically mean either, depending on context, because Polish present tense can describe:

• an action happening now
• a general characteristic
• a habitual action

In this sentence, without extra context, it most naturally sounds like a general statement about the car’s braking performance:
The car brakes well.

Polish usually does not need a separate subject pronoun like it when the subject is already stated.

Since samochód is present, there is no need to add anything else.

Even without the noun, hamuje already tells you it is 3rd person singular, but Polish often leaves the subject understood if context is clear.

Yes, Polish word order is more flexible than English, but the neutral, most natural order here is:

Samochód dobrze hamuje.

Other orders are possible, for example:

• Dobrze hamuje samochód.
• Hamuje dobrze.

But these usually sound more marked, poetic, contrastive, or context-dependent. For a basic neutral sentence, Samochód dobrze hamuje is best.

Here it is used intransitively.

That means there is no direct object. The sentence means the car itself has good braking performance.

Compare:

• Samochód dobrze hamuje. = The car brakes well.
• Kierowca hamuje samochód. = The driver is braking the car.

So hamować can be used both ways, depending on meaning.

Hamować is imperfective.

That is why hamuje works naturally for:

• ongoing action
• repeated action
• general ability or tendency

If you wanted a perfective verb, you would normally use something like zahamować for a completed act of braking.

Very roughly:

• hamować = to be braking / to brake in general
• zahamować = to brake once / to apply the brakes successfully

In this sentence, the imperfective is exactly what you want.

A rough English-friendly pronunciation is:

sa-MO-khoot DOB-zhe ha-MOO-ye

More accurately in Polish:

• samochód → sa-MO-hut
  
  • ch sounds like a hard h / Scottish loch
  • final ó sounds like u
• dobrze → DOB-zhe
  
  • rz/ż sounds like a voiced zh sound
• hamuje → ha-MOO-ye
  
  • j sounds like English y

A more phonetic version is:
[saˈmɔxut ˈdɔbʐɛ xaˈmujɛ]

They are related, but not the same.

• hamuje = brakes / is braking
• zatrzymuje się = stops / is stopping

A car can hamować without coming to a complete stop immediately. Braking is the action of slowing down; stopping is the result.

So:

• Samochód dobrze hamuje = The car brakes well.
• Samochód zatrzymuje się = The car stops.

Yes. Auto is also a very common word for car.

So both are possible:

• Samochód dobrze hamuje.
• Auto dobrze hamuje.

The meaning is the same. Samochód may sound slightly more standard or formal, while auto is very common in everyday speech.

Because Polish nouns change form depending on case.

The dictionary form is samochód (nominative singular), but other cases look different:

• samochód — nominative
• samochodu — genitive
• samochodowi — dative
• samochód — accusative
• samochodem — instrumental
• samochodzie — locative

In your sentence, the noun is the subject, so nominative samochód is used.