Sprawdzam zarówno numer zamówienia, jak i środek płatniczy.

It means both ... and ....

So:

• zarówno numer zamówienia, jak i środek płatniczy
  = both the order number and the means/method of payment

It is a fixed paired construction in Polish. You normally use both parts together:

• zarówno X, jak i Y

It sounds a bit more formal or emphatic than just i = and.

Because in Polish, the paired construction zarówno ..., jak i ... is normally written with a comma separating the two parts:

• zarówno X, jak i Y

So the comma here is standard punctuation, not optional decoration.

Sprawdzam is:

• 1st person singular
• present tense
• from the imperfective verb sprawdzać

So it means:

• I check
• I am checking

Which English version fits best depends on context.

A useful point: Polish imperfective present can cover both the simple and continuous present in English.

Because Polish often drops subject pronouns when the verb already makes the subject clear.

In sprawdzam, the ending -am tells you the subject is I.

So:

• Sprawdzam = I am checking / I check

You can add ja if you want emphasis or contrast:

• Ja sprawdzam zarówno numer zamówienia, jak i środek płatniczy.
  = I’m the one checking both the order number and the payment method.

But in a neutral sentence, leaving ja out is more natural.

Because Polish has no articles.

English needs words like:

• a
• an
• the

Polish does not. So numer zamówienia can mean:

• an order number
• the order number

and context tells you which is meant.

The same applies to środek płatniczy.

They are the direct objects of sprawdzam, so they are in the accusative case.

However, for masculine inanimate singular nouns, the accusative often looks exactly like the nominative.

That is why you get:

• numer → accusative numer
• środek → accusative środek

The adjective płatniczy agrees with środek, and for masculine inanimate singular, its accusative also looks like the nominative:

• środek płatniczy

So even though these words are objects, their forms do not visibly change here.

Because Polish often uses the genitive after another noun to show a relationship like of in English.

So:

• numer zamówienia
  literally: number of the order

Here:

• zamówienie = order
• zamówienia = of the order / genitive singular

This pattern is very common in Polish. Compare:

• numer telefonu = phone number
• adres e-maila = email address
• koniec filmu = the end of the film

So numer zamówienia is the normal Polish structure.

Literally, it means payment means or payment instrument.

Depending on context, it may be translated as:

• means of payment
• payment method
• payment instrument

It sounds a bit formal or technical. In everyday language, people may more often say things like:

• metoda płatności = payment method
• forma płatności = form of payment

So środek płatniczy is correct, but it has a somewhat formal/administrative flavor.

Yes, absolutely.

That version is simpler and very natural:

• Sprawdzam numer zamówienia i środek płatniczy.

Using zarówno ..., jak i ... adds emphasis to the idea that both items are being checked.

So the difference is roughly:

• X i Y = X and Y
• zarówno X, jak i Y = both X and Y

The second version is a bit more deliberate or formal.

Yes, Polish word order is fairly flexible, but not every order sounds equally neutral.

The given sentence:

• Sprawdzam zarówno numer zamówienia, jak i środek płatniczy.

is natural and neutral.

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

• Zarówno numer zamówienia, jak i środek płatniczy sprawdzam.

But that sounds more marked, as if you are stressing exactly what you are checking.

So for ordinary use, the original order is a good model.

The perfective partner of sprawdzać is sprawdzić.

So:

• Sprawdzam ... = I am checking / I check ...
• Sprawdzę ... = I will check / I’ll verify ...

Example:

• Sprawdzę zarówno numer zamówienia, jak i środek płatniczy.
  = I will check both the order number and the means of payment.

This is a classic Polish aspect pair:

• sprawdzać = imperfective
• sprawdzić = perfective

A natural negative version would be:

• Nie sprawdzam ani numeru zamówienia, ani środka płatniczego.

This shows two important things:

1. Polish often uses ani ..., ani ... for neither ... nor ... in negative structures.
2. With negation, direct objects often change from accusative to genitive.

So compare:

• Sprawdzam numer zamówienia.
• Nie sprawdzam numeru zamówienia.

and:

• Sprawdzam środek płatniczy.
• Nie sprawdzam środka płatniczego.

That case change is very important in Polish.

Here it is singular.

• dictionary form: zamówienie = order
• genitive singular: zamówienia

Even though -a / -ia endings can sometimes look plural to English-speaking learners, here it is definitely singular because the phrase means:

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

If it were plural, the meaning would be different: something like number of orders.