Судоходная компания предлагает ночной рейс.

Yes, in this sentence судоходная компания means shipping company or shipping line.

A useful nuance:

• судоходный literally relates to navigation by ships
• it can also mean navigable in other contexts, for example судоходная река = a navigable river

So with компания, it means a company involved in ship transport.

Because it is an adjective agreeing with компания.

• компания is feminine
• it is singular
• here it is in the nominative case because it is the subject

So the adjective must also be:

• feminine
• singular
• nominative

That gives судоходная.

Its basic dictionary form is the masculine:

• судоходный

Compare:

• судоходный рейс — masculine
• судоходная компания — feminine
• судоходное судно — neuter
• судоходные компании — plural

Because компания is the subject of the sentence — the thing doing the action.

The verb is предлагает = offers, and the company is the one offering.

So:

• Судоходная компания = subject, nominative
• ночной рейс = object, accusative

Because предлагать usually takes a direct object in the accusative case.

So Russian says:

• предлагать рейс = to offer a route/service/trip
• предлагать помощь = to offer help
• предлагать услугу = to offer a service

No preposition is needed.

If you want to add the person receiving the offer, that person is often in the dative:

• Компания предлагает пассажирам ночной рейс.
• The company offers passengers a night service.

It is in the accusative case, because it is the direct object of предлагает.

But рейс is:

• masculine
• singular
• inanimate

For inanimate masculine singular nouns, the accusative has the same form as the nominative.

So:

• nominative: рейс
• accusative: рейс

That is why it looks unchanged.

Because ночной agrees with рейс.

Here рейс is:

• masculine
• singular
• accusative

And for inanimate masculine singular adjectives, the accusative form is the same as the nominative.

So:

• nominative masculine singular: ночной
• accusative masculine singular inanimate: ночной

That is why you get ночной рейс.

Other forms would be:

• ночная поездка — feminine
• ночное путешествие — neuter
• ночные рейсы — plural

It can mean night or overnight, depending on context.

In transport contexts, ночной рейс often means:

• a service that happens at night
• or an overnight service/journey

So the exact English translation may vary:

• night service
• overnight service
• night trip
• overnight sailing

The Russian adjective itself does not always force one single English choice.

Because рейс is usually a scheduled trip/service/run made by some means of transport.

It is commonly used for:

• planes
• buses
• ferries
• ships
• other regular transport services

By contrast:

• поездка = a trip/ride taken by a person
• путешествие = a journey, often broader or longer
• рейс = a scheduled transport service

So with a shipping company, рейс is a very natural choice.

предлагает is:

• present tense
• 3rd person singular
• imperfective aspect

Its infinitive is:

• предлагать = imperfective, to offer

So предлагает means:

• offers
• is offering

depending on context.

Why imperfective? Because this kind of sentence usually describes:

• a general fact
• a regular service
• something currently available

The perfective partner is:

• предложить

For example:

• Компания предложит новый рейс. = The company will offer a new service.

Yes. Russian word order is more flexible than English word order.

The sentence as given:

• Судоходная компания предлагает ночной рейс.

is the most neutral order:

• subject + verb + object

You can change the order for emphasis, for example:

• Ночной рейс предлагает судоходная компания.

That can sound more marked, with focus on ночной рейс.

So the original order is the best neutral version for a textbook sentence.

Because Russian has no articles.

So Судоходная компания can mean:

• a shipping company
• the shipping company

and ночной рейс can mean:

• a night service
• the night service

Context tells you which one is intended.

This is very normal in Russian, and learners have to get used to reading definiteness from context rather than from articles.

The main stress is:

• судохОдная компАния предлагАет ночнОй рейс

A rough pronunciation guide:

• судоходная ≈ soo-da-KHOD-na-ya
• компания ≈ kam-PA-nee-ya
• предлагает ≈ preed-la-GA-yet
• ночной ≈ nach-NOY
• рейс ≈ rays

A couple of pronunciation notes:

• Unstressed о is often pronounced closer to a
• рейс has a sound similar to English rays
• Russian stress is important and must be learned word by word