Ελέγχουν όχι μόνο αριθμό διαβατηρίου αλλά και ημερομηνία λήξης.

Ελέγχουν means they check / they are checking.

It is the 3rd person plural form of the verb ελέγχω (to check, inspect, verify).

Greek often leaves out the subject pronoun when it is obvious from the verb ending, so Ελέγχουν by itself already means they check. You do not need to add αυτοί unless you want emphasis.

Because Greek is a pro-drop language, which means subject pronouns are often omitted.

So:

• Ελέγχουν = They check
• Αυτοί ελέγχουν = They check (with extra emphasis, like they do it)

In ordinary Greek, leaving out the pronoun is the most natural choice.

This is the standard Greek pattern for not only ... but also ...

So:

• όχι μόνο αριθμό διαβατηρίου
• αλλά και ημερομηνία λήξης

= not only passport number but also expiration date

A useful pattern to remember is:

• όχι μόνο X αλλά και Y = not only X but also Y

They are in the accusative case because they are the direct objects of Ελέγχουν.

They are the things being checked:

• check what? → αριθμό διαβατηρίου
• check what else? → ημερομηνία λήξης

So the basic structure is:

• Ελέγχουν
  • direct object(s)

That is why you see:

• αριθμός → αριθμό in the accusative
• ημερομηνία stays ημερομηνία in the accusative because many feminine nouns in -α look the same in nominative and accusative singular

They are in the genitive case because they depend on the nouns before them.

So:

• αριθμός διαβατηρίου = passport number
• ημερομηνία λήξης = expiration date / date of expiry

This is a very common Greek structure:

• noun + genitive noun

It often corresponds to English noun combinations like:

• student card
• car door
• passport number

In Greek, that relationship is often shown with the genitive rather than by simply putting two nouns together.

Greek often omits articles in concise, formal, bureaucratic, or list-like language.

So this sentence sounds a bit like an official statement or instruction:

• Ελέγχουν όχι μόνο αριθμό διαβατηρίου αλλά και ημερομηνία λήξης.

If you added articles, it would still be grammatical:

• Ελέγχουν όχι μόνο τον αριθμό διαβατηρίου αλλά και την ημερομηνία λήξης.

That version may sound a little fuller or more explicit.
The article-less version is very natural in official or compact wording.

Yes, literally it is something like number of passport, but in natural English it means passport number.

Greek commonly expresses this idea with:

• main noun + genitive

So:

• αριθμός διαβατηρίου = passport number
• ημερομηνία λήξης = expiration date

It is better to understand these as natural noun phrases, not translate them word-for-word every time.

Greek word order is more flexible than English.

This sentence begins with the verb:

• Ελέγχουν ...

That is perfectly normal in Greek, especially in formal statements, descriptions, or when the action is the main focus.

You could also rearrange it, for example:

• Ελέγχουν όχι μόνο τον αριθμό διαβατηρίου αλλά και την ημερομηνία λήξης.
• Όχι μόνο αριθμό διαβατηρίου αλλά και ημερομηνία λήξης ελέγχουν.

But the original order is natural and clear.

No. The normal expression is:

• όχι μόνο ... αλλά και ...

That fixed order is important.

So use:

• όχι μόνο X αλλά και Y

not:

• μόνο όχι X αλλά και Y

The Greek phrase works as a set expression, just like English not only ... but also ...

Here are the main dictionary forms:

• ελέγχω = to check, inspect
• όχι = not
• μόνο = only
• αριθμός = number
• διαβατήριο = passport
• αλλά = but
• και = also / and
• ημερομηνία = date
• λήξη = expiration, ending

Forms used in the sentence:

• Ελέγχουν from ελέγχω
• αριθμό from αριθμός
• διαβατηρίου from διαβατήριο
• ημερομηνία from ημερομηνία
• λήξης from λήξη

Yes, absolutely. Ημερομηνία λήξης is a very common phrase meaning expiration date.

You will see it on:

• passports
• IDs
• food packaging
• medicine
• cards and official documents

So it is worth learning as a chunk:

• ημερομηνία λήξης = expiration date

Similarly, αριθμός διαβατηρίου is also a useful phrase to memorize as a unit.

It can mean either, depending on context.

Greek present tense often covers both:

• they check
• they are checking

So:

• Ελέγχουν όχι μόνο αριθμό διαβατηρίου αλλά και ημερομηνία λήξης.

could mean:

• They check not only the passport number but also the expiration date or
• They are checking not only the passport number but also the expiration date

The surrounding context tells you which English translation sounds best.