Yayın numarası dosyada yazıyor.

Here is the breakdown:

• yayın = publication, broadcast, issue, release, depending on context
• numarası = its number / number of
  
  • from numara
    • -sı
• dosyada = in the file
  
  • from dosya
    • -da
• yazıyor = is written / it says / it appears in writing

So the structure is roughly:

• yayın numarası = publication number
• dosyada = in the file
• yazıyor = is written / says

A very literal feeling is something like The publication number is written in the file.

Because yayın numarası is a very common Turkish noun-compound pattern.

In Turkish, when one noun modifies another noun, the second noun often takes the 3rd person possessive-looking suffix:

• telefon numarası = phone number
• kimlik numarası = ID number
• yayın numarası = publication number

So:

• yayın = publication
• numara = number
• yayın numarası = publication number

Even though English does not show this with an extra ending, Turkish usually does in this type of construction.

Dosyada is dosya + -da, and -da/-de is the locative case, meaning in, on, at depending on context.

So:

• dosya = file
• dosyada = in the file

This suffix changes according to vowel harmony and consonants:

• evde = at home
• okulda = at school
• çantada = in the bag

Here, dosyada means the information is located inside the file.

Yes, yazıyor literally comes from yazmak = to write, and in many contexts it does mean is writing.

But with things like signs, labels, documents, screens, and written information, Turkish often uses yazıyor in the sense of:

• it says
• it is written
• it appears written

For example:

• Kapıda çıkış yazıyor. = It says exit on the door.
• Ekranda hata yazıyor. = It says there is an error on the screen.

So in your sentence, yazıyor does not mean someone is actively writing right now. It means the publication number is written there / shown there.

Yes. Yayın numarası dosyada yazılı is also possible.

The difference is roughly this:

• yazıyor = it says / it is written there
• yazılı = written, in written form

So:

• dosyada yazıyor sounds a bit more like it says that in the file
• dosyada yazılı sounds a bit more adjectival or descriptive: it is written in the file

In many everyday situations, both can work.
Yazıyor is very common in spoken Turkish when referring to written information.

The subject is yayın numarası.

So the sentence is about the publication number, and the predicate is dosyada yazıyor.

In English, learners sometimes expect a dummy subject like it, but Turkish does not need that here. The sentence naturally works as:

• [Yayın numarası] [dosyada yazıyor].

That is, The publication number is written in the file / The file says the publication number depending on how naturally you want to express it in English.

Turkish does not have articles like the and a/an in the same way English does.

So yayın numarası can mean:

• the publication number
• a publication number

Which one feels right depends on context.

In real usage, this sentence would usually be understood as the publication number, because it sounds like a specific known number being referred to.

No, Turkish word order is flexible, although some orders are more neutral than others.

The given sentence:

• Yayın numarası dosyada yazıyor.

is natural and neutral enough.

You could also hear:

• Dosyada yayın numarası yazıyor.

This puts a little more focus on dosyada first, like In the file, the publication number is written.

In Turkish, the word right before the verb often gets extra focus. So word order can shift depending on emphasis, even when the basic meaning stays similar.

It could be dosyanın içinde, but that is more explicit.

Compare:

• dosyada = in the file
• dosyanın içinde = inside the file

In many situations, dosyada is enough and sounds simpler and more natural.
Dosyanın içinde is used when you want to stress physical or literal inside-ness more clearly.

So the sentence with dosyada is normal and idiomatic.

It depends on context. Yayın can cover several related meanings, such as:

• broadcast
• publication
• release
• issue

So yayın numarası might mean something like:

• publication number
• broadcast number
• issue number

The exact English wording depends on the situation. Turkish often leaves this kind of detail to context.

A native speaker would usually understand it as something like:

• The publication number is written in the file.
• The file contains the publication number.
• The publication number is listed in the file.

The key point is that yazıyor here is not about the act of writing. It is about information being present in written form.