Muayene randevusu muayene istasyonunda.

Because Turkish often leaves out the present-tense to be in simple noun/adjective/location sentences.

So:

• Muayene randevusu muayene istasyonunda. = The inspection appointment is at the inspection station.

There is no separate word for is here. This is completely normal in Turkish.

You will see the copula more clearly in other contexts, for example:

• Muayene randevusu muayene istasyonundaydı. = The inspection appointment was at the inspection station.
• Muayene randevusu muayene istasyonunda değil. = The inspection appointment is not at the inspection station.

So in the present tense, third person, Turkish often just uses the two parts side by side.

Muayene randevusu is a Turkish noun compound.

It is made of:

• muayene = inspection / examination
• randevu = appointment

But in Turkish, when one noun modifies another noun, the second noun usually takes a compound ending:

• randevu → randevusu

So:

• muayene randevusu = inspection appointment / appointment for inspection

This pattern is very common:

• otobüs durağı = bus stop
• yemek masası = dining table
• muayene randevusu = inspection appointment

So muayene randevu would sound ungrammatical or incomplete in standard Turkish.

Not exactly. In Turkish, nouns often modify other nouns directly.

So in:

• muayene randevusu
• muayene istasyonu

the word muayene is still basically a noun, but it functions as the first part of a noun compound.

English often uses noun + noun combinations too:

• car door
• school bus
• inspection station

So this is not an adjective in the usual sense; it is a noun used attributively.

The ending -nda shows location: in / at / on.

The base expression is:

• muayene istasyonu = inspection station

To say at the inspection station, Turkish adds the locative ending:

• muayene istasyonu
  • -nda
• muayene istasyonunda

So muayene istasyonunda means:

• at the inspection station
• in the inspection station
  depending on context, though at is probably the most natural translation here.

These are different grammatical pieces.

1) randevusu

This is:

• randevu
  • -su

The -su is the compound/possessive-type ending used in this noun-compound structure.
Because randevu ends in a vowel, Turkish inserts a buffer consonant s:

• randevu + u → randevusu

2) istasyonunda

This is built from:

• istasyonu
  • -nda

Here the word already has that compound ending:

• muayene istasyonu = inspection station

Then Turkish adds the locative ending -da / -de.
Because the noun already has that possessive/compound ending, Turkish inserts a buffer n before the case ending:

• istasyonu + da → istasyonunda

So the short version is:

• s often appears as a buffer before a possessive/compound ending after a vowel
• n often appears before a case ending after a possessed form

Because it belongs to two different compounds:

• muayene randevusu = inspection appointment
• muayene istasyonu = inspection station

Even though English speakers may want to avoid repetition, Turkish often repeats the noun when it is part of two separate compound expressions.

So the sentence is structurally:

• [inspection appointment] [at the inspection station]

The repetition is normal and helps keep the meaning precise.

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

So muayene randevusu can be understood from context as:

• the inspection appointment
• an inspection appointment
• sometimes just inspection appointment in a general sense

In many real contexts, English will translate it with the, because the situation is already known.

If Turkish wants to be more explicitly indefinite, it can use bir:

• bir muayene randevusu = an inspection appointment

But Turkish often leaves this to context.

Yes. This is a very natural neutral order for a verbless sentence of this type:

• subject/topic: Muayene randevusu
• location predicate: muayene istasyonunda

So the structure is basically:

• [The inspection appointment] [at the inspection station].

Turkish word order is flexible, but this version is straightforward and unmarked. If you move things around, the emphasis can change, and sometimes you would prefer a fuller sentence with an explicit verb.

It can be a full sentence, because Turkish allows these present-tense nominal sentences without an explicit is.

So yes, it is grammatical as a complete sentence.

That said, in real life it can also sound like the kind of concise wording you might see in:

• a schedule
• a notice
• an app interface
• a short informational message

In more expanded spoken Turkish, someone might also say something like:

• Muayene randevusu muayene istasyonunda olur.
• Muayene randevusu muayene istasyonunda yapılır.

But the shorter original sentence is still perfectly normal.

Yes, if the context already makes it clear which station you mean.

So:

• Muayene randevusu istasyonda.

can work in context, meaning something like:

• The inspection appointment is at the station.

But this is less specific.
The full version:

• Muayene randevusu muayene istasyonunda.

explicitly says it is at the inspection station, not just any station.

So the longer version is clearer, especially when there could be ambiguity.