Номер этажа указан в лифте.

Because Russian often uses the pattern noun + genitive noun to mean X of Y.

So:

номер этажа = the number of the floor = the floor number

Here номер is the main noun, and этажа is in the genitive singular of этаж.

A few similar examples:

• дверь комнаты = the door of the room
• крыша дома = the roof of the house
• центр города = the center of the city

Указан is the short-form passive participle of указать.

In this sentence it means something like:

• is indicated
• is shown
• is specified
• is listed

So Номер этажа указан means The floor number is indicated/shown.

This short form is commonly used in Russian to describe a state or result.

Compare:

• указанный номер = the indicated/specified number
  
  • this is the full form, used like an adjective before a noun
• номер указан = the number is indicated
  
  • this is the short form, used as the predicate

In Russian, the verb to be is usually omitted in the present tense.

So where English says:

• The floor number is indicated in the elevator

Russian says:

• Номер этажа указан в лифте

There is no separate present-tense word for is here.

This is very normal in Russian:

• Он студент = He is a student
• Дверь открыта = The door is open
• Адрес указан = The address is indicated

Because в + the prepositional case is used for location: in, inside, within.

So:

• в лифте = in the elevator

The noun лифт changes to лифте in the prepositional case.

Compare:

• в доме = in the house
• в комнате = in the room
• в лифте = in the elevator

If it were motion into the elevator, Russian would use the accusative:

• в лифт = into the elevator

Because указан agrees with номер, which is masculine singular.

Agreement here is with the main noun номер, not with этажа.

Forms:

• указан = masculine singular
• указана = feminine singular
• указано = neuter singular
• указаны = plural

Examples:

• Номер указан = The number is indicated
• Таблица указана = The table is indicated
• Место указано = The place is indicated
• Данные указаны = The data are indicated

Yes, it is a normal and clear expression.

Literally it means number of the floor, which is exactly how Russian often builds this kind of phrase.

Depending on context, Russian may also simply use этаж if the meaning is obvious:

• Лифт показывает этаж = The elevator shows the floor

But if you specifically mean the numeral or label for the floor, номер этажа works well.

Because номер usually means an identifying number, label, or assigned number, while число is more like a numerical quantity or mathematical number.

A floor marker such as 2, 5, or 15 is treated as a label, so номер is the natural choice.

Compare:

• номер квартиры = apartment number
• номер телефона = phone number
• номер страницы = page number

But:

• число is used more in math or abstract counting contexts

So for floor number, номер is the better word.

Yes. Russian word order is fairly flexible.

This sentence:

Номер этажа указан в лифте

could also be rearranged as:

В лифте указан номер этажа

The basic meaning stays the same, but the emphasis changes a little.

• Номер этажа указан в лифте focuses first on the floor number
• В лифте указан номер этажа focuses first on the location

Russian often moves elements around for emphasis, topic, or style.

Yes, a little.

Указан is perfectly normal Russian, but it has a somewhat formal, neutral, or informational tone. It is common in notices, instructions, official writing, and descriptions.

In everyday speech, people might also use other verbs depending on the situation, such as:

• показан = shown
• обозначен = marked
• написан = written

But указан is completely grammatical and natural if the idea is that the floor number is officially indicated or displayed somewhere in the elevator.

It can mean either, depending on context.

Указан is fairly broad. It simply says that the floor number is indicated in the elevator. That could mean:

• written on a panel
• marked near the buttons
• shown on a screen
• displayed in some other way

If you wanted to be more specific, Russian could use a more precise verb:

• написан = written
• показан на дисплее = shown on a display
• обозначен = marked

So указан leaves the exact method open.