Ночной рейс отправляется из паромного терминала.

Because рейс is a masculine singular noun, and the adjective has to agree with it.

• рейс = masculine
• nominative singular masculine adjective ending here = -ой
• so: ночной рейс

If the noun were feminine, the adjective would change too, for example:

• ночная смена = night shift

Рейс is in the nominative singular because it is the subject of the sentence — the thing that is departing.

You can think of the structure like this:

• Ночной рейс = the night service / night departure
• отправляется = departs
• из паромного терминала = from the ferry terminal

So рейс is the subject, and subjects are normally in the nominative.

Because the preposition из requires the genitive case.

The dictionary form is:

• паромный терминал = ferry terminal

After из, both words change to genitive singular:

• паромный → паромного
• терминал → терминала

So:

• из паромного терминала = from the ferry terminal

This is a very common pattern in Russian:

• из дома = from the house
• из города = from the city
• из аэропорта = from the airport

Рейс usually means a scheduled trip / service / run made by some form of transport.

Depending on context, it can mean:

• a flight
• a ferry service
• a bus run
• a scheduled trip in general

In this sentence, because it mentions a ferry terminal, рейс probably means something like an overnight service or scheduled departure, not necessarily an airplane flight.

So рейс is broader than English flight.

Отправляется is a very common verb for transport departures. It comes from отправляться, which often means:

• to depart
• to set off
• to leave

In transport language, it is standard and natural for scheduled departures:

• Поезд отправляется в 8:00. = The train departs at 8:00.
• Автобус отправляется от вокзала. = The bus departs from the station.

Here it is:

• отправляется = it departs

because рейс is singular.

Russian often uses the present tense for timetables, schedules, and fixed future events, just like English sometimes does:

• The train leaves at 6 tomorrow.
• Our flight departs at noon.

So:

• Ночной рейс отправляется... can refer to a scheduled future departure

This is completely normal in Russian.

The -ся makes the verb отправляться, which is the standard intransitive form used for things like trains, planes, ships, and services departing.

Compare the idea:

• отправить что-то = to send something
• отправиться / отправляться = to set off / to depart

In this sentence, рейс is not sending something; the service itself is departing, so отправляется is the natural form.

You do not need to translate -ся literally every time. Here it is just part of the normal verb meaning departs.

Here из is the best choice because it means from inside / out of a place.

• из терминала = from the terminal

Compare:

• из = from inside a place
• от = from near something or someone
• с = from off a surface, or in some idiomatic expressions

Examples:

• из аэропорта = from the airport
• от здания = from the building
• с платформы = from the platform

With терминал, из is the normal choice.

It means ferry terminal.

Russian often uses an adjective where English uses a noun modifier:

• паромный терминал = ferry terminal
• literally, something like ferry-related terminal

So паромного is just the genitive form of паромный after из.

Yes. Russian word order is flexible, although different orders can change the emphasis.

The original sentence:

• Ночной рейс отправляется из паромного терминала.

This is a neutral, natural order.

You could also say:

• Из паромного терминала отправляется ночной рейс.

This puts more focus on where it departs from.

So the meaning stays basically the same, but the information focus changes.

Because Russian has no articles.

So Russian does not have separate words for:

• a
• an
• the

Whether English uses a night service, the night service, or the overnight departure depends on context, not on a separate Russian word.

That is why:

• Ночной рейс can mean a night service or the night service, depending on the situation.

A helpful stress-marked version is:

Ночно́й ре́йс отправля́ется из па́ромного терминáла.

Rough pronunciation guide:

• Ночно́й = nach-NOY
• ре́йс = rays
• отправля́ется = at-prav-LYAE-tsa
• из = ees / iz
• па́ромного = PA-raam-na-va
• терминáла = teer-mee-NA-la

A couple of useful notes:

• г in паромного is pronounced like v in normal speech: паромнова
• из may sound more like из or ис depending on the next sound, but learners can safely say iz

Sometimes yes, but отправляется is the most standard and neutral choice for schedules and transport announcements.

• отправляется = formal, standard, timetable-style
• уходит = literally goes away / leaves, sometimes used for transport too, but it can sound more conversational

For example:

• Поезд отправляется в 22:00. = very standard
• Поезд уходит в 22:00. = possible in conversation

In your sentence, отправляется is the safest and most natural choice.