Kelnerka przynosi drugą filiżankę i pyta, czy potrzebujemy jeszcze jednej łyżeczki.

Kelnerka means waitress, while kelner means waiter. The ending -ka often marks a feminine noun in Polish.

So:

• kelner = waiter
• kelnerka = waitress

The sentence tells us that the person bringing the cup and asking the question is female.

Przynosi is the present tense of the imperfective verb przynosić = to bring / to be bringing.

• przynosi = is bringing / brings
• przyniesie = will bring (future, perfective)

In a sentence like this, Polish often uses the present tense to describe what is happening in a scene:

• Kelnerka przynosi... i pyta...
  = The waitress brings... and asks...

This can sound a bit like a narrative present in English: describing events as they happen.

Because filiżanka is a feminine noun, and here it is the direct object of przynosi. Direct objects often go into the accusative case.

So:

• nominative: druga filiżanka = a second cup
• accusative: drugą filiżankę = a second cup as the object of brings

Both words change:

• druga → drugą
• filiżanka → filiżankę

This is very normal with feminine nouns in Polish.

Literally, druga means second.

So drugą filiżankę is literally a second cup.

In natural English, depending on context, this may also be translated as another cup, but the Polish word itself is specifically related to second.

Here czy introduces an indirect yes/no question.

The waitress is asking whether we need one more spoon, so Polish uses:

• pyta, czy... = asks whether / asks if...

Examples:

• Pyta, czy chcemy kawy. = She asks if we want coffee.
• Pyta, czy potrzebujemy... = She asks whether we need...

So czy here works like English if or whether in an indirect question.

Potrzebujemy is the 1st person plural present tense of potrzebować = to need.

So:

• potrzebuję = I need
• potrzebujesz = you need
• potrzebuje = he/she/it needs
• potrzebujemy = we need
• potrzebujecie = you all need
• potrzebują = they need

In this sentence, potrzebujemy means we need.

Because in Polish, subject pronouns are often omitted when the verb form already makes the subject clear.

• potrzebujemy already means we need
• you do not need to say my potrzebujemy unless you want emphasis

So:

• potrzebujemy = we need
• my potrzebujemy = we need with extra emphasis, something like we are the ones who need

This is very common in Polish.

Because potrzebować normally takes the genitive case in standard Polish.

So after potrzebujemy (we need), the thing needed appears in the genitive:

• nominative: jedna łyżeczka = one teaspoon
• genitive: jednej łyżeczki

That is why the sentence has:

• potrzebujemy jeszcze jednej łyżeczki

not:

• potrzebujemy jeszcze jedna łyżeczka

Both words are in the genitive singular feminine:

• jedna → jednej
• łyżeczka → łyżeczki

This is because of potrzebujemy / potrzebować, which requires the genitive in standard Polish.

So:

• nominative: jedna łyżeczka
• genitive: jednej łyżeczki

The phrase means one teaspoon in the form required by the verb.

Here it means one more teaspoon or another teaspoon.

The word jeszcze can mean different things depending on context, including:

• still
• yet
• more / another

In this sentence, the natural meaning is:

• czy potrzebujemy jeszcze jednej łyżeczki
  = whether we need one more teaspoon

So jeszcze is adding the idea of an additional one.

The base noun is łyżeczka, which usually means teaspoon.

It is historically related to a diminutive, but in modern everyday Polish, łyżeczka is the normal standard word for a small spoon / teaspoon. It does not necessarily sound especially cute or affectionate.

Compare:

• łyżka = spoon / tablespoon-sized spoon
• łyżeczka = teaspoon / small spoon

In the sentence, łyżeczki is simply the genitive singular form of łyżeczka.

Yes, something like czy potrzebujemy jeszcze jednej łyżeczki and czy potrzebujemy kolejnej łyżeczki can be similar, but the nuance is a little different.

• jeszcze jednej łyżeczki = one more teaspoon / another teaspoon
• kolejnej łyżeczki = an additional / next teaspoon

Jeszcze jednej sounds very natural and conversational here. It focuses on adding one more item. Kolejnej can sound a little more formal or more explicitly sequential.

Yes, Polish word order is relatively flexible, but this version is the most neutral and natural.

• Kelnerka przynosi drugą filiżankę i pyta...

This is a straightforward subject + verb + object structure.

You could change the word order for emphasis, but the neutral version is best for learners. For example:

• Drugą filiżankę przynosi kelnerka...

This would sound more marked, as if emphasizing the second cup or the waitress.

So the original order is the normal, unmarked one.

Not exactly.

• filiżanka = cup, usually a teacup or coffee cup, often smaller and more delicate
• kubek = mug

So drugą filiżankę suggests a more typical café-style cup, not a large mug.

Yes. Czy can introduce a direct yes/no question too.

For example:

• Czy potrzebujemy jeszcze jednej łyżeczki?
  = Do we need one more teaspoon?

In your sentence, though, it appears inside an indirect question after pyta:

• pyta, czy potrzebujemy...
  = she asks if/whether we need...

So the function is similar, but the whole clause is embedded under asks.