Αυτό είναι το ασφαλιστήριο συμβόλαιο.

Because ασφαλιστήριο συμβόλαιο is neuter singular, and the demonstrative Αυτό is the neuter singular form of this.

The three basic singular forms are:

• αυτός = this (masculine)
• αυτή = this (feminine)
• αυτό = this (neuter)

Since συμβόλαιο is a neuter noun, Αυτό is the matching form.

A word-by-word breakdown:

• Αυτό = this
• είναι = is
• το = the (neuter singular)
• ασφαλιστήριο = insurance / insuring, here modifying the noun
• συμβόλαιο = contract, policy

So το ασφαλιστήριο συμβόλαιο is literally something like the insurance contract/policy, i.e. the insurance policy.

είναι is the 3rd person singular of είμαι = to be.

So:

• είμαι = I am
• είσαι = you are
• είναι = he/she/it is

In this sentence, είναι means is.

A useful extra point: Greek often drops personal subject pronouns, but here Αυτό is not an optional subject pronoun like it. It is the demonstrative this, so you keep it if you want to say this is.

Because the noun phrase is definite: the insurance policy.

In Greek, definite noun phrases normally take the definite article:

• το συμβόλαιο = the contract/policy
• το ασφαλιστήριο συμβόλαιο = the insurance policy

If you wanted an insurance policy, you would usually say:

• ένα ασφαλιστήριο συμβόλαιο

So το here is simply the neuter singular form of the.

In this sentence, it functions like an adjective modifying συμβόλαιο.

So:

• συμβόλαιο = contract/policy
• ασφαλιστήριο συμβόλαιο = insurance policy

But in real usage, ασφαλιστήριο is also very often used on its own as a noun meaning insurance policy:

• Πού είναι το ασφαλιστήριο; = Where is the insurance policy?

So a learner will often meet both:

• το ασφαλιστήριο συμβόλαιο = full, more explicit form
• το ασφαλιστήριο = shorter everyday form

Because ασφαλιστήριο συμβόλαιο is the normal established expression.

Greek adjective position can vary in some cases, but not every order sounds equally natural. Here the pre-noun position is the standard one:

• ασφαλιστήριο συμβόλαιο = normal
• συμβόλαιο ασφαλιστήριο = unnatural or at least not the usual way to say it

So it is best to learn ασφαλιστήριο συμβόλαιο as a fixed term.

They are in the nominative.

With είμαι and other forms of to be, Greek normally uses the nominative for both the subject and the predicate noun:

• Αυτό = nominative
• το ασφαλιστήριο συμβόλαιο = nominative

A detail that can confuse learners: in the neuter singular, the nominative and accusative often look the same. So even though the form is the same, the function here is nominative.

A rough English-style guide:

• Αυτό = af-TO
• είναι = EE-ne
• το = to
• ασφαλιστήριο = a-sfa-li-STEE-rio
• συμβόλαιο = sim-VO-le-o

Whole sentence:

• af-TO EE-ne to a-sfa-li-STEE-rio sim-VO-le-o

Two pronunciation notes:

1. αυ in Αυτό is pronounced af here, because it comes before τ, a voiceless sound.
2. β in συμβόλαιο is pronounced like English v, not like English b.

Yes. In standard written Greek, the accent marks are part of correct spelling.

So you should write:

• Αυτό
• είναι
• ασφαλιστήριο
• συμβόλαιο

They show which syllable is stressed:

• αυτό
• είναι
• ασφαλιστήριο
• συμβόλαιο

For learners, they are especially helpful because Greek stress is important and can’t just be guessed from English habits.

Yes, very often.

Since ασφαλιστήριο is commonly used by itself to mean insurance policy, this shorter version is natural in many contexts:

• Αυτό είναι το ασφαλιστήριο.

The full version:

• Αυτό είναι το ασφαλιστήριο συμβόλαιο.

is more explicit and a bit more formal or careful.

You would normally say:

• Αυτό είναι ένα ασφαλιστήριο συμβόλαιο.

The main change is the article:

• το = the
• ένα = an / a

So:

• Αυτό είναι το ασφαλιστήριο συμβόλαιο. = This is the insurance policy.
• Αυτό είναι ένα ασφαλιστήριο συμβόλαιο. = This is an insurance policy.