Δεδομένου ότι άρχισε η επιβίβαση οχημάτων, ο καταπέλτης μένει ανοιχτός.

Yes. In practice, δεδομένου ότι is best learned as a fixed connector meaning given that, since, or seeing that.

A learner does not usually need to build it from scratch each time. In this sentence, it introduces the reason/background for the main statement:

• Δεδομένου ότι άρχισε η επιβίβαση οχημάτων, ...
• Given that vehicle boarding has begun, ...

It is especially common in formal, official, or written Greek.

Because this is a frozen formal construction.

Historically, δεδομένου is a participial form in the genitive, but in modern Greek, when you see δεδομένου ότι, you usually treat it as a set phrase rather than something that changes to match a noun in the sentence.

So:

• δεδομένου ότι = a fixed formal linker
• not something you normally adjust for gender or number here

For most learners, the simplest approach is: memorize δεδομένου ότι as one unit.

Άρχισε is the aorist of αρχίζω and means began / started.

The aorist is used because the sentence presents the start of boarding as a completed event that now has a consequence:

• boarding started
• therefore the ramp remains open

So the structure is roughly:

• first event: άρχισε η επιβίβαση οχημάτων
• current resulting situation: ο καταπέλτης μένει ανοιχτός

Using the aorist here is very natural in announcements and operational language.

Because αρχίζω can be followed in two different ways:

1. by a noun phrase

   • Άρχισε η επιβίβαση οχημάτων
   • literally, the boarding of vehicles began

2. by να + verb

   • Άρχισαν να επιβιβάζονται οχήματα
   • Vehicles began to board / be boarded

In your sentence, Greek uses the noun επιβίβαση rather than a second verb. This sounds more compact and formal.

Because Greek uses the definite article much more often than English does.

So where English might say:

• boarding began

Greek naturally says:

• άρχισε η επιβίβαση

Here, η επιβίβαση is the subject of άρχισε.

This is very normal Greek, especially with abstract nouns and event nouns such as:

• η επιβίβαση = boarding
• η φόρτωση = loading
• η αναχώρηση = departure

Οχημάτων is genitive plural of όχημα.

It depends on επιβίβαση and means:

• η επιβίβαση οχημάτων = the boarding of vehicles

This is a very common Greek pattern:

• noun of action + genitive
• φόρτωση αποσκευών = loading of luggage
• μεταφορά επιβατών = transport of passengers
• έκδοση εισιτηρίων = issuing of tickets

There is no article before οχημάτων because it is being used in a general sense: vehicles in general, not a previously identified set of vehicles.

If the speaker wanted to be more specific, they might say:

• η επιβίβαση των οχημάτων = the boarding of the vehicles

In this context, καταπέλτης does not mean a medieval catapult.

In ferry, port, or vehicle-loading language, ο καταπέλτης means the loading ramp — the ramp that vehicles use to get on or off the ship.

So this is a specialized transport/maritime meaning.

That is an important vocabulary point, because outside this context, an English speaker might guess the wrong meaning.

Because μένει ανοιχτός means stays open or remains open, not just is open.

Compare:

• είναι ανοιχτός = it is open
• μένει ανοιχτός = it remains/stays open

So μένει emphasizes that the ramp continues in that state because of the situation described.

In official notices, this kind of wording is very common, because it focuses on the ongoing operational condition.

Because ανοιχτός is an adjective agreeing with ο καταπέλτης.

• ο καταπέλτης = masculine singular nominative
• therefore: ανοιχτός = masculine singular nominative

Greek adjectives agree with the noun they describe in:

• gender
• number
• case

So:

• ο καταπέλτης μένει ανοιχτός
• but η πόρτα μένει ανοιχτή
• and το παράθυρο μένει ανοιχτό

It can be changed.

The sentence begins with the reason clause:

• Δεδομένου ότι άρχισε η επιβίβαση οχημάτων, ο καταπέλτης μένει ανοιχτός.

But Greek could also place the main clause first:

• Ο καταπέλτης μένει ανοιχτός, δεδομένου ότι άρχισε η επιβίβαση οχημάτων.

Both are grammatical.
Putting δεδομένου ότι... first sounds especially natural in formal written language, because it sets up the reason before the main statement.

Because the sentence begins with a subordinate clause:

• Δεδομένου ότι άρχισε η επιβίβαση οχημάτων,
• then the main clause follows:
• ο καταπέλτης μένει ανοιχτός.

The comma helps separate the introductory reason clause from the main statement. This is standard punctuation.

Yes, it sounds fairly formal, like something from a notice, announcement, or operational instruction.

More everyday Greek might use simpler connectors, for example:

• Αφού άρχισε η επιβίβαση των οχημάτων, ο καταπέλτης μένει ανοιχτός.
• Εφόσον άρχισε η επιβίβαση των οχημάτων, ο καταπέλτης μένει ανοιχτός.

Or a less nominal, more verbal style:

• Άρχισε η επιβίβαση των οχημάτων, οπότε ο καταπέλτης μένει ανοιχτός.

Your original sentence is perfectly good Greek, but its tone is definitely more official/formal than casual speech.