Πριν πας στο γραφείο, κοίτα αν το διαβατήριό σου είναι ακόμα έγκυρο και όχι ληγμένο.

After πριν (before), Greek normally uses a non-past verb form to refer to something that has not happened yet.

So:

• πριν πας = before you go

Greek does not use θα after πριν here.
Using θα would sound wrong in this structure.

You may also sometimes see πριν να πας, but πριν πας is very common and natural.

Yes. Κοίτα is the 2nd person singular imperative, so it means look or, in this context, check.

Here it is telling one person to do something:

• κοίτα = check / look

In everyday Greek, κοίτα is very common and conversational. It can be used both literally (look!) and more broadly as check.

A slightly fuller form you may also hear is κοίταξε. Both are used.

Greek κοιτάω / κοιτάζω can mean more than just physically looking at something. Depending on context, it can also mean:

• look at
• check
• see whether
• make sure

So in this sentence, κοίτα αν... is very natural Greek for check whether...

It is similar to English, where look if is not standard, but check if is.

Here αν means if / whether in an indirect question.

So:

• κοίτα αν το διαβατήριό σου είναι ακόμα έγκυρο
  = check whether your passport is still valid

This is not really a condition in the sense of If it rains, we will stay home.
Instead, it introduces something to be checked.

A good way to think of it here is:

• αν = whether

Στο is a contraction of:

• σε + το = στο

So:

• στο γραφείο = to the office / at the office, depending on context

Here, with πας (you go), it means to the office.

Also, γραφείο is a neuter noun, and after σε the noun appears in the accusative.
For this noun, the accusative and nominative look the same:

• το γραφείο
• στο γραφείο

This happens because σου is an enclitic word, meaning it leans on the previous word for pronunciation.

The base word is:

• διαβατήριο

When σου is added, Greek spelling often adds an extra written accent:

• διαβατήριό σου

This helps show the correct stress pattern in pronunciation.

So this is not a different word; it is just the normal spelling of your passport in this context.

Because they agree with το διαβατήριο, which is:

• neuter
• singular

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

So:

• το διαβατήριο = neuter singular
• έγκυρο = neuter singular
• ληγμένο = neuter singular

If the noun were masculine or feminine, the adjective endings would change too.

Because δεν normally negates a verb, while όχι can negate a word or phrase more directly.

Here the sentence has:

• είναι ακόμα έγκυρο και όχι ληγμένο

The όχι is specifically contrasting the adjective ληγμένο:

• valid and not expired

If you wanted to negate the whole verb phrase, you could say:

• δεν είναι ληγμένο = it is not expired

So both are possible in Greek, but they work slightly differently:

• όχι ληγμένο = focuses on the adjective
• δεν είναι ληγμένο = negates the whole clause

Here ακόμα means still:

• είναι ακόμα έγκυρο = it is still valid

Yes, ακόμη is also possible. In many contexts, ακόμα and ακόμη mean the same thing.

In everyday speech, ακόμα is very common.
So you could also hear:

• είναι ακόμη έγκυρο

Both are natural.

Yes. The forms show that it is addressed to one person, in an informal way:

• πας = you go
• κοίτα = check

If you wanted to say the same thing to more than one person, or more formally to one person, you would use plural/formal forms, for example:

• Πριν πάτε στο γραφείο, κοιτάξτε αν το διαβατήριό σας είναι ακόμα έγκυρο και όχι ληγμένο.

So the original sentence is singular and informal.

Έγκυρο is an adjective meaning valid.

Ληγμένο is originally a participial form, but in everyday Greek it functions very much like an adjective meaning expired.

So in this sentence, both words are acting as predicate adjectives after είναι:

• το διαβατήριό σου είναι έγκυρο
• το διαβατήριό σου είναι ληγμένο

For a learner, the simplest way to understand them here is: both are adjective-like words describing the passport.