Organisasjonsnummeret står på fakturaen.

Because Norwegian very often forms compound nouns by joining words together.

Here:

• organisasjon = organization
• nummer = number

So they combine into organisasjonsnummer = organization number. The -s- in the middle is a common linking element in Norwegian compounds.

Then -et is added at the end to make it definite: organisasjonsnummeret = the organization number.

In Norwegian, the definite article is usually attached to the end of the noun instead of being a separate word like English the.

So:

• et organisasjonsnummer = an organization number
• organisasjonsnummeret = the organization number

The ending -et is used because the main noun here is nummer, which is a neuter noun. In compounds, the gender of the whole word is normally determined by the last part of the compound.

For the same reason: Norwegian marks definiteness by adding an ending.

So:

• en faktura = an invoice
• fakturaen = the invoice

In this sentence, the speaker means a specific invoice, not just any invoice, so the definite form fakturaen is used.

Yes, stå literally means to stand, but Norwegian uses it much more broadly than English does.

When something is written or printed on a page, sign, form, or document, Norwegian often says it stands there:

• Det står på skiltet. = It says on the sign.
• Navnet står på listen. = The name is on the list.

So Organisasjonsnummeret står på fakturaen means that the organization number is written/printed/shown on the invoice. This is very natural Norwegian.

Because Norwegian usually uses på for text or information that appears on a document, page, form, sign, or similar surface.

So:

• på fakturaen = on the invoice

Using i would sound less natural here. Norwegian sees this as information appearing on the document rather than being inside it in a physical sense.

The sentence has a very basic main-clause order:

• Organisasjonsnummeret = subject
• står = verb
• på fakturaen = prepositional phrase

So it is:

Subject + Verb + Adverbial

This is normal Norwegian word order in a simple statement.

You can also move the prepositional phrase to the front:

På fakturaen står organisasjonsnummeret.

That is also correct. Norwegian main clauses usually keep the verb in second position.

Yes, that would be understandable.

But står på fakturaen is usually more idiomatic when you mean that something is written or printed there. It gives a stronger sense of visible text on the document.

• er på fakturaen = more neutral, simply is on the invoice
• står på fakturaen = more natural when referring to written information

So the original sentence sounds more natural in everyday Norwegian.

Yes, very often. This is a common pattern in Norwegian.

For example:

• Adressen står på nettsiden. = The address is on the website.
• Prisen står på menyen. = The price is on the menu.
• Navnet ditt står på lista. = Your name is on the list.
• Det står i e-posten is also possible, but that uses i because an email is often treated more like text content in a message.

So with documents, signs, pages, forms, and similar things, stå is a very useful verb to learn.