Zero klientów czeka.

Because after zero, Polish uses the genitive plural form of the noun.

• singular dictionary form: klient
• nominative plural: klienci
• genitive plural: klientów

So:

• klienci czekają = the customers are waiting
• zero klientów czeka = zero customers are waiting / no customers are waiting

This is one of the big differences between English and Polish number expressions.

In English, customers is plural, so English uses are waiting.
In Polish, expressions with zero are normally treated grammatically like a singular quantity expression, so the verb is 3rd person singular:

• Zero klientów czeka.

That is why you get czeka, not czekają.

A very similar pattern happens with larger numbers too:

• Pięć osób czeka. = Five people are waiting.

Czeka is the 3rd person singular present tense form of czekać (to wait).

So:

• czekam = I wait / I am waiting
• czekasz = you wait
• czeka = he/she/it waits — and also the form used here with zero klientów

Even though the meaning is plural in English, the Polish verb form is singular because of the number expression.

It is grammatical and natural, especially when you want to stress the exact number 0:

• in statistics
• on a screen or display
• in business or service contexts
• when reporting numbers

For example, it can sound like a queue-status message.

In everyday conversation, Polish often prefers a negative structure such as:

• Żaden klient nie czeka. = No customer is waiting.

So zero klientów czeka is correct, but it can sound a bit more numerical or factual than the more everyday negative version.

No. If you use zero, you do not need nie.

• Zero klientów czeka. = correct
• Żaden klient nie czeka. = also correct, but this is a different structure

With żaden, standard Polish requires nie.
With zero, the sentence can stay affirmative in form.

It is the genitive plural of klient.

Here are the useful forms:

• klient = customer
• klienci = customers (nominative plural)
• klientów = of customers / customers after zero and many other numerals

The ending -ów is a very common genitive plural ending for masculine nouns.

Yes, Polish word order is flexible.

You can say:

• Zero klientów czeka.
• Czeka zero klientów.

Both are possible. The difference is mainly one of emphasis and information structure.

• Zero klientów czeka can sound like the focus is on the number.
• Czeka zero klientów can sound more like There are zero customers waiting.

A good rule for learners: keep zero klientów together as one unit.

In the past tense, Polish usually makes this pattern even more visible:

• Zero klientów czekało. = Zero customers were waiting.

Notice the verb is still singular, and in the past it appears in the neuter singular form czekało.

So you can compare:

• present: Zero klientów czeka.
• past: Zero klientów czekało.

This helps show that Polish is treating zero klientów as a quantity expression, not as a normal plural subject like klienci.

The grammar is different because the subject is built differently.

• Klienci czekają.
  Here klienci is a normal nominative plural subject, so the verb is plural: czekają.

• Zero klientów czeka.
  Here zero klientów is a number expression, so the noun becomes genitive plural and the verb is singular: czeka.

So the key contrast is:

• normal plural subject -> klienci czekają
• quantity expression -> zero klientów czeka