Το βιομετρικό διαβατήριο είναι καινούριο.

Here is the sentence broken down:

• Το = the
• βιομετρικό = biometric
• διαβατήριο = passport
• είναι = is
• καινούριο = new

So structurally it is:

• Το βιομετρικό διαβατήριο = the biometric passport
• είναι καινούριο = is new

This is a very standard Greek sentence pattern:
subject + είναι + adjective

Because διαβατήριο is a neuter noun.

In Greek, nouns have grammatical gender:

• ο for masculine
• η for feminine
• το for neuter

Since διαβατήριο is neuter, its article is το.

So:

• το διαβατήριο = the passport

The adjective before it also matches that gender, which is why you get βιομετρικό.

Because they are both in the neuter singular form here.

In Greek, adjectives must agree with the noun they describe in:

• gender
• number
• case

So since διαβατήριο is neuter singular, the adjective must also be neuter singular:

• masculine: βιομετρικός
• feminine: βιομετρική
• neuter: βιομετρικό

Here the noun is το διαβατήριο, so the correct form is το βιομετρικό διαβατήριο.

Because καινούριο is a predicate adjective and it still has to agree with the noun.

Even though it comes after είναι, it still describes το βιομετρικό διαβατήριο, so it must match it.

Since διαβατήριο is neuter singular, you need:

• καινούριος for masculine
• καινούρια / καινούργια for feminine
• καινούριο / καινούργιο for neuter

So:

• Το διαβατήριο είναι καινούριο. = The passport is new.

In a normal sentence like this, yes, you need it.

Greek usually uses the verb είμαι (to be) in this kind of statement:

• Το διαβατήριο είναι καινούριο.

You generally cannot just say:

• Το διαβατήριο καινούριο.

That may appear in headlines, notes, or very informal speech, but it is not the normal full sentence pattern for learners to copy.

So for standard Greek, keep είναι.

Yes. This is the normal and natural order.

In Greek, an adjective often comes before the noun:

• το βιομετρικό διαβατήριο

That is the straightforward way to say the biometric passport.

Greek word order is somewhat flexible, but this version is the one a learner should use.

In a full sentence, Greek usually prefers the article when talking about a specific item:

• Το βιομετρικό διαβατήριο είναι καινούριο.

Without the article, βιομετρικό διαβατήριο sounds more like:

• a label
• a dictionary form
• a general category
• part of a headline or sign

So if you mean the biometric passport, keep το.

It is in the nominative singular.

Why? Because it is the subject of the sentence:

• Το βιομετρικό διαβατήριο = the thing that is new

The nominative is the normal case for the subject.

Since the adjective βιομετρικό goes with the noun, it appears in the same case as well.

Yes, you could also say:

• Το βιομετρικό διαβατήριο είναι νέο.

Both καινούριο and νέο can mean new, but there is a slight difference in feel:

• καινούριο often means new, brand-new, not old/used
• νέο can mean new in a broader sense, including newly introduced or recent

In everyday speech, καινούριο is very common when talking about an object being newly made or recently obtained.

So in this sentence, καινούριο sounds very natural.

Both are correct.

You may hear or see:

• καινούριο
• καινούργιο

They are just variant forms of the same adjective (new). The same is true in other genders too:

• masculine: καινούριος / καινούργιος
• feminine: καινούρια / καινούργια
• neuter: καινούριο / καινούργιο

So this sentence could also be:

• Το βιομετρικό διαβατήριο είναι καινούργιο.

That is equally acceptable.

A rough pronunciation guide is:

To vee-oh-mee-tree-KO thee-ah-vah-TEE-ree-oh EE-neh keh-NOO-ree-oh

A few helpful points:

• β in Modern Greek sounds like v
• δ sounds like the th in this
• αι sounds like e
• ει sounds like ee
• The stressed syllables are:
  • βιομετρικό
  • διαβατήριο
  • είναι
  • καινούριο

Listening to native audio is especially helpful with Greek stress.

Yes. That means:

• The passport is biometric.

That sentence focuses on the passport’s type or feature.

Your original sentence:

• Το βιομετρικό διαβατήριο είναι καινούριο.

starts with the biometric passport as one noun phrase, and then says that it is new.

So the two sentences are both correct, but they emphasize different things:

• Το διαβατήριο είναι βιομετρικό. → the passport is biometric
• Το βιομετρικό διαβατήριο είναι καινούριο. → the biometric passport is new

A little, yes, but the original order is the most natural for a learner.

Standard order:

• Το βιομετρικό διαβατήριο είναι καινούριο.

You might also hear emphasis-based variations in speech, but Greek does not change word order randomly. The default sentence you have is clear, neutral, and idiomatic.

So it is best to learn this as the normal model:

• article + adjective + noun + είναι + adjective