Numer zamówienia jest na potwierdzeniu zamówienia.

Because the sentence contains two different noun phrases:

• numer zamówienia = order number
• potwierdzeniu zamówienia = on the order confirmation

In both places, zamówienia is the genitive singular of zamówienie (order).

This is very common in Polish: one noun is used to specify another noun, where English often uses a noun directly as an adjective-like modifier.

So:

• numer zamówienia literally means number of the order
• potwierdzenie zamówienia literally means confirmation of the order

Because after na the case depends on the meaning.

Here, na means on in a location sense, so it takes the locative case.

• na potwierdzeniu = on the confirmation

If it were about movement toward something, Polish would often use the accusative:

• położyć coś na stół = to put something onto the table

But in your sentence, nothing is moving. The order number already is on the confirmation, so the locative is used:

• potwierdzenie → potwierdzeniu after na

Because it follows the preposition na in the sense of location.

The base form is:

• potwierdzenie = confirmation

After na meaning on, it changes to locative singular:

• na potwierdzeniu = on the confirmation

This is a normal pattern for many neuter nouns ending in -enie or -cie.

In both places, zamówienia is genitive singular.

Dictionary form:

• zamówienie = order

Genitive singular:

• zamówienia = of the order

So:

• numer zamówienia = the number of the order / order number
• potwierdzenie zamówienia = confirmation of the order / order confirmation

Yes:

• Numer — number; masculine singular nominative
• zamówienia — of the order; genitive singular of zamówienie
• jest — is; 3rd person singular of być
• na — on
• potwierdzeniu — locative singular of potwierdzenie (confirmation)
• zamówienia — again, genitive singular of zamówienie

So the structure is:

• Numer zamówienia = subject
• jest = verb
• na potwierdzeniu zamówienia = location phrase

Yes, in some situations Polish can omit jest (is), especially in informal speech or short labels:

• Numer zamówienia na potwierdzeniu zamówienia.

But in a full normal sentence, especially in careful or standard written Polish, jest is natural and correct:

• Numer zamówienia jest na potwierdzeniu zamówienia.

So for learners, keeping jest is usually the safest choice.

Yes, Polish word order is more flexible than English, because case endings show the grammatical relationships.

The neutral order here is:

• Numer zamówienia jest na potwierdzeniu zamówienia.

But other orders are possible for emphasis, for example:

• Na potwierdzeniu zamówienia jest numer zamówienia.

This sounds more like On the order confirmation, there is the order number.

The original version is the most straightforward if you want to say what the subject is and where it is located.

Usually na potwierdzeniu zamówienia is the better choice here.

Why? Because Polish often uses na for information appearing on a document, page, screen, label, or form.

Examples:

• na stronie = on the page
• na liście = on the list
• na fakturze = on the invoice

So:

• na potwierdzeniu zamówienia = on the order confirmation

Using w potwierdzeniu zamówienia would sound more like in the order confirmation, which is less natural if you simply mean printed or written on the document.

Not exactly.

• potwierdzenie alone means confirmation
• potwierdzenie zamówienia means specifically order confirmation

In context, Polish often drops the second noun if it is obvious:

• Numer zamówienia jest na potwierdzeniu.

That can work if everyone already knows you mean the order confirmation. But the full phrase is clearer.

Yes, it matters for case endings and agreement.

• numer is masculine
• zamówienie is neuter
• potwierdzenie is neuter

In this sentence:

• numer stays in nominative as the subject
• zamówienia is genitive singular
• potwierdzeniu is locative singular

The verb jest is singular because the subject numer is singular.

The given sentence is correct, but depending on context, Polish speakers might also say:

• Numer zamówienia jest na potwierdzeniu.
• Znajdziesz numer zamówienia na potwierdzeniu zamówienia. = You will find the order number on the order confirmation.
• Numer zamówienia znajduje się na potwierdzeniu zamówienia. = The order number is located on the order confirmation.

The original sentence is clear and grammatical; it just repeats zamówienia, which is normal but can feel a little heavy stylistically.

A rough English-friendly guide:

• zamówienia ≈ za-moo-VYE-nya
• potwierdzeniu ≈ pot-fyer-DZE-nyoo

A few pronunciation notes:

• ó sounds like u
• ie often sounds like ye
• dz is pronounced together as one sound
• ń is a soft n, similar to the ny in canyon

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

• za-mó-WIE-nia
• po-twier-DZE-niu

Yes, out of context, numer zamówienia can mean either:

• the order number
• an order number
• the number of the order

Polish has no articles like a or the, so definiteness comes from context.

In your sentence, English would usually translate it as the order number because the situation is specific: a particular order confirmation is being discussed.