Müşteri numarası faturada yazıyor.

Because müşteri numarası is a common Turkish noun compound meaning customer number.

In this pattern:

• the first noun stays plain: müşteri = customer
• the second noun takes a 3rd-person possessive ending: numara → numarası

So:

• müşteri numarası = customer number

This is very normal in Turkish:

• telefon numarası = phone number
• kimlik numarası = ID number
• oda numarası = room number

So numarası does not mean his/her number here in the usual sense; it is part of the compound structure.

Good question. Turkish has two similar-looking patterns:

1. Belirtisiz noun compound
   müşteri numarası = customer number
   This usually names a type/category/label.

2. Genitive + possessed form
   müşterinin numarası = the customer’s number
   This refers more directly to a specific customer and that customer’s number.

So:

• müşteri numarası = customer number / customer ID number
• müşterinin numarası = the customer’s number

In your sentence, müşteri numarası sounds like the standard label you would see on a bill or form.

The ending is the 3rd-person possessive suffix, and after a vowel Turkish usually inserts a buffer -s-.

So:

• numara
  • -(s)ı → numarası

Why -ı and not another vowel? Because of vowel harmony.

The basic pattern is:

• -(s)ı
• -(s)i
• -(s)u
• -(s)ü

The form depends on the last vowel of the word. Since numara has a as its last vowel, the correct form is -sı.

Faturada is fatura + -da.

• fatura = invoice / bill
• -da = locative case, meaning in / on / at depending on context

So faturada means something like:

• on the invoice
• in the invoice
• on the bill

In English, on the invoice is the most natural translation here.

Turkish often uses one case ending where English uses different prepositions.

Because the locative suffix changes according to vowel harmony and consonant voicing.

The locative has four forms:

• -da
• -de
• -ta
• -te

For fatura:

• the last vowel is a, so we need a-type harmony: -da or -ta
• the word ends in a vowel, so there is no devoicing issue, and d stays d

So:

• fatura
  • -da = faturada

Yes, the basic verb yazmak means to write, and yazıyor often means is writing.

But in Turkish, yazıyor is also very commonly used for text that appears somewhere, with a meaning like:

• is written
• it says
• appears in writing

So in sentences like this, yazıyor does not usually mean someone is actively writing at this moment. It means the information is there in written form.

For example:

• Kapıda “Kapalı” yazıyor. = It says “Closed” on the door.
• Etikette fiyat yazıyor. = The price is written on the label. / It shows the price on the label.

That is the same idea here.

Yes, but the nuance changes a bit.

• yazıyor = it is written / it says / it appears there as text
  Very natural in everyday speech.
• yazılı = written, in written form
  More adjectival.
• yazılmış = has been written / was written
  More result-focused or passive in feel.

So these are all possible in different contexts:

• Müşteri numarası faturada yazıyor.
• Müşteri numarası faturada yazılı.
• Müşteri numarası faturaya yazılmış.

Your original sentence is a very natural everyday way to say that the customer number appears on the invoice.

The subject is müşteri numarası.

So the structure is:

• müşteri numarası = subject
• faturada = location
• yazıyor = verb

In other words, the sentence is about the customer number, and it says where it appears: on the invoice.

Because Turkish normally puts the finite verb at the end of the sentence.

A very common Turkish order is:

• subject + place/time + verb

So:

• Müşteri numarası
  • faturada
    • yazıyor

That is completely natural.

Turkish word order is somewhat flexible, though. If you change the order, you usually change emphasis rather than the core meaning. For example:

• Faturada müşteri numarası yazıyor.

This is also possible, with a bit more focus on the invoice.

Because Turkish does not have a definite article like English the.

So Turkish often leaves definiteness to context.

For example:

• müşteri numarası can mean the customer number or a customer number, depending on context
• faturada can mean on the invoice or on an invoice, depending on the situation

In this sentence, the context usually makes it natural in English to say the customer number is on the invoice.

Technically, Turkish -da/-de covers a general location idea, so it does not force the same in/on/at distinction that English does.

So faturada could correspond to:

• in the invoice
• on the invoice
• sometimes even on the bill

In English, since text is printed on a document, on the invoice is the most natural choice.

Normally, no.

Even though yazıyor is the present continuous form, in this kind of sentence it is understood more like:

• is written
• is shown
• appears there

So a Turkish speaker would usually understand it as a statement about what the invoice contains, not about someone currently doing the act of writing.