Номер рейса указан в паромном терминале.

Because after номер Russian normally uses the genitive case.

So:

• номер = number
• рейс = trip / service / flight / sailing
• номер рейса = the number of the trip/service/flight

This is the same pattern as:

• номер телефона = phone number
• номер паспорта = passport number
• номер поезда = train number

So рейс changes to рейса because it depends on номер.

Рейс is a general transport word meaning a scheduled trip or run made by some vehicle.

Depending on context, it can mean:

• a flight for a plane
• a train service
• a bus run
• a ferry sailing / ferry service

Since the sentence says в паромном терминале (in the ferry terminal), рейс here is understood as a ferry service / sailing / departure, not an airplane flight.

So even if you may first learn рейс as flight, it is actually broader than that.

Указан is the short-form passive participle of указать.

In this sentence it means something like:

• is indicated
• is shown
• is listed

So:

• номер рейса указан = the service number is indicated / shown

This is a very common Russian way to express a state or result, especially in formal or written language.

Compare:

• Адрес указан в письме. = The address is given in the letter.
• Дата указана ниже. = The date is indicated below.

Because указан agrees with номер, which is masculine singular.

Agreement here works like this:

• номер — masculine singular → указан
• дата — feminine singular → указана
• место — neuter singular → указано
• данные — plural → указаны

Examples:

• Номер указан.
• Дата указана.
• Место указано.
• Подробности указаны.

Since номер is masculine, the correct form is указан.

Russian normally omits the verb to be in the present tense.

So English:

• The flight number is indicated...

but Russian simply says:

• Номер рейса указан...

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

If you wanted past or future, Russian would use forms of быть:

• Номер рейса был указан... = The flight number was indicated...
• Номер рейса будет указан... = The flight number will be indicated...

But in the present, zero copula is normal.

It is the prepositional case after в because the sentence is talking about location.

• в
  • prepositional = in / at a place

So:

• терминал → в терминале
• паромный терминал → в паромном терминале

This means in the ferry terminal or sometimes at the ferry terminal, depending on how naturally you would phrase it in English.

A useful comparison:

• в терминал = into the terminal (motion, accusative)
• в терминале = in the terminal (location, prepositional)

Here there is no movement, just location, so в терминале is correct.

Because adjectives must agree with the noun they describe in gender, number, and case.

The noun is:

• терминал — masculine singular

After в for location, it becomes prepositional singular:

• в терминале

So the adjective must also become prepositional masculine singular:

• паромный → паромном

That gives:

• в паромном терминале

This is standard adjective-noun agreement.

Yes, it is essentially a passive-style sentence.

It focuses on the result:

• Номер рейса указан... = The service number is indicated...

rather than on who did the action.

An active version would be something like:

• В паромном терминале указали номер рейса. = They indicated the service number in the ferry terminal.

But Russian often prefers the shorter participle construction when the agent is unimportant or unknown.

Yes. Russian word order is more flexible than English, although the basic meaning stays the same.

The original sentence:

• Номер рейса указан в паромном терминале.

A possible alternative:

• В паромном терминале указан номер рейса.

Both are grammatical. The difference is mainly emphasis:

• Номер рейса указан... starts with the topic flight/service number
• В паромном терминале... starts with the location

Russian often moves words around to highlight what is new, important, or already known from context.

Yes, somewhat. Указан is common and natural, but it has a slightly formal, informational, or written feel.

It is especially common in:

• signs
• announcements
• instructions
• official texts
• websites
• schedules

In more everyday spoken Russian, people might also use other verbs depending on context, such as:

• написан = written
• показан = shown
• есть constructions in some contexts
• можно увидеть = can be seen

But for notices and formal information, указан is very typical.

Yes. Russian в here literally means in, but in natural English the best translation may be either in the ferry terminal or at the ferry terminal, depending on context.

For example:

• if you mean physically inside the building, in the ferry terminal fits well
• if you mean generally at that location, at the ferry terminal may sound more natural in English

Russian often leaves that distinction less sharply defined than English does.