Kundnumret står på räkningen.

Because Swedish normally forms compound nouns as a single word.

• kund = customer
• nummer = number
• kundnummer = customer number

Then Swedish adds the definite ending to the whole noun:

• ett kundnummer = a customer number
• kundnumret = the customer number

This is very typical in Swedish. English often writes these as two words, but Swedish usually combines them.

In Swedish, the is often built into the noun as a suffix.

So instead of a separate word like English the customer number, Swedish says:

• kundnummer = customer number
• kundnumret = the customer number

The ending -et is the definite form here. Swedish often does this with nouns instead of using a separate article.

Because nummer is an ett-word in Swedish:

• ett nummer = a number
• numret = the number

The compound keeps the gender of its final part, so:

• ett kundnummer = a customer number
• kundnumret = the customer number

A useful rule: in Swedish compounds, the last part decides the grammatical gender and the inflection.

Literally, yes: står comes from stå, which means to stand.

But in this sentence, it is being used idiomatically. When Swedish talks about words or information written on something, stå often means:

• be written
• appear
• be stated

So Kundnumret står på räkningen means that the customer number is written on the bill/invoice.

This is very natural Swedish. English usually would not say the customer number stands on the bill, but Swedish does.

You might be understood, but står is much more natural here.

Compare:

• Kundnumret står på räkningen = The customer number is written on the bill / appears on the bill.
• Kundnumret är på räkningen = The customer number is on the bill.

The version with är sounds more general and less idiomatic for written information. står specifically suggests that the information is printed or written there.

Because Swedish usually uses på for something written or printed on a surface, page, form, bill, sign, and so on.

So:

• på räkningen = on the bill

This matches English quite well here. Swedish often thinks of the bill as a physical or printed surface where information appears.

Because the sentence is talking about a specific bill/invoice: the bill.

• en räkning = a bill / an invoice
• räkningen = the bill / the invoice

So:

• på räkningen = on the bill

As with kundnumret, the definite meaning is shown by an ending instead of a separate word for the.

Not always exactly. Räkning often means bill or invoice, depending on context.

In everyday use:

• räkning can mean a bill you need to pay
• faktura is often a more formal word for invoice

In many contexts, either translation may work, but räkning often feels a bit more everyday.

Yes, but Swedish keeps the verb in second position in main clauses.

The original sentence is:

• Kundnumret står på räkningen.

If you move på räkningen to the front, you get:

• På räkningen står kundnumret.

That is still correct. The verb står stays in the second position.

This is a very important Swedish rule called V2 word order.

A rough guide:

• står sounds approximately like stor in British English, but with a Swedish å sound.
• räkningen is roughly REK-ning-en, though the Swedish ä is not exactly the same as English e.

A few sound notes:

• å in står is a rounded vowel, somewhat like the vowel in British law for many speakers.
• ä in räkningen is more open than English ay.
• The g in räkning is not strongly pronounced as a separate hard g sound in normal speech; the word flows more like räkning-en.

If you want to sound natural, it is especially useful to learn the whole phrase as a chunk:

• Kundnumret står på räkningen.

You would normally make the nouns indefinite:

• Ett kundnummer står på en räkning.

That means A customer number is written on a bill, though it sounds less natural as an isolated sentence because it is very unspecific.

More commonly, you would hear the definite version when talking about an actual document:

• Kundnumret står på räkningen.

That sounds more natural because both the customer number and the bill are understood as specific.