Nie cierpię gorzkiej kawy bez mleka.

Because after a negated verb in Polish, the direct object often changes from the accusative to the genitive.

• Positive: Cierpię gorzką kawę / Lubię kawę
• Negative: Nie cierpię gorzkiej kawy / Nie lubię kawy

So here:

• kawa = nominative
• kawę = accusative
• kawy = genitive

Since the sentence has nie cierpię, kawa becomes kawy.

Because adjectives must agree with the noun they describe in gender, number, and case.

Here, kawa is:

• feminine
• singular
• genitive

So the adjective gorzka changes to gorzkiej to match it.

Compare:

• gorzka kawa = bitter coffee (nominative)
• gorzką kawę = bitter coffee (accusative)
• gorzkiej kawy = bitter coffee (genitive)

Because the preposition bez always takes the genitive case.

So:

• mleko = nominative
• mleka = genitive

That is why you say:

• bez mleka = without milk
• bez cukru = without sugar
• bez wody = without water

Nie cierpię literally means I can’t stand or I hate.

The verb is cierpieć. In modern Polish, nie cierpieć czegoś is a strong way to say you really dislike something.

It is stronger than:

• nie lubię = I don’t like

So:

• Nie lubię gorzkiej kawy = I don’t like bitter coffee
• Nie cierpię gorzkiej kawy = I can’t stand bitter coffee / I hate bitter coffee

Not exactly.

Both can be translated as I hate, but the tone is a bit different:

• nie cierpię = I can’t stand, I really dislike
• nienawidzę = I hate, often stronger and more intense

For everyday dislikes, nie cierpię is very common and natural:

• Nie cierpię zimna.
• Nie cierpię czekać.

Nienawidzę can sound more emotionally loaded.

Literally, it means bitter coffee without milk.

So the focus is on coffee that is both:

• gorzka = bitter
• bez mleka = without milk

It does not automatically mean black coffee in the standard lexical sense.

Useful distinction:

• czarna kawa = black coffee
• kawa bez mleka = coffee without milk
• gorzka kawa = bitter coffee

Sometimes coffee without milk may be bitter, but grammatically these are separate ideas.

Because Polish has no articles.

So kawa can mean:

• coffee
• a coffee
• the coffee

Which meaning is intended depends on context.

In this sentence, gorzkiej kawy is understood generically: coffee of that kind, not one specific cup.

No, Polish word order is fairly flexible, though some orders sound more neutral than others.

The most natural neutral version here is:

• Nie cierpię gorzkiej kawy bez mleka.

You could also move things around for emphasis, for example:

• Gorzkiej kawy bez mleka nie cierpię.
  This puts extra emphasis on bitter coffee without milk.

But for a learner, the original order is the safest and most natural.

It is the 1st person singular present tense form of cierpieć.

So:

• cierpię = I suffer / I can’t stand
• nie cierpię = I can’t stand / I hate

A few present-tense forms:

• cierpię = I
• cierpisz = you
• cierpi = he/she/it
• cierpimy = we
• cierpicie = you plural
• cierpią = they

Yes. In Polish, a singular noun is often used to talk about something in a general sense.

So gorzkiej kawy here means bitter coffee in general, not necessarily one single serving.

This is very normal in Polish:

• Nie lubię herbaty. = I don’t like tea.
• Nie jem mięsa. = I don’t eat meat.
• Potrzebuję wody. = I need water.

A rough pronunciation guide is:

Nyeh chyer-PYEH gor-SKYEY KA-vih bez MLEH-kah

A few tips:

• nie sounds roughly like nyeh
• ci in cierpię sounds like a soft chy
• rz in gorzkiej sounds like the zh sound in measure
• w in Polish sounds like English v
• stress usually falls on the second-to-last syllable:
  • cierPIĘ
  • GORZkiej
  • MLEka

Yes, if you want to change the meaning.

• bez mleka = without milk
• z mlekiem = with milk

So:

• Nie cierpię gorzkiej kawy bez mleka. = I can’t stand bitter coffee without milk.
• Nie cierpię gorzkiej kawy z mlekiem. = I can’t stand bitter coffee with milk.

Notice that z takes the instrumental here:

• mleko → mlekiem

They are:

• nie = not
• cierpieć = to suffer; to be unable to stand
• gorzki / gorzka / gorzkie = bitter
• kawa = coffee
• bez = without
• mleko = milk

In the sentence, some of them appear in changed forms because of case and agreement:

• cierpię from cierpieć
• gorzkiej from gorzka
• kawy from kawa
• mleka from mleko