Τα απεριόριστα λεπτά ομιλίας είναι στο πρόγραμμα συμβολαίου.

Because it agrees with λεπτά, which is neuter plural.

• λεπτό = minute
• λεπτά = minutes

The adjective απεριόριστος / απεριόριστη / απεριόριστο changes form to match gender, number, and case. Here it must match λεπτά, so we get:

• τα απεριόριστα λεπτά

That whole phrase is neuter plural nominative.

Τα is the definite article for neuter plural nouns in the nominative and accusative.

So:

• το λεπτό = the minute
• τα λεπτά = the minutes

Since λεπτά is plural and neuter, the article must also be plural neuter:

• τα απεριόριστα λεπτά

In Greek, articles are used very often, even in places where English might say simply unlimited minutes without the.

It literally means minutes of speech/talking, but in natural English it usually means talk minutes or calling minutes.

Breakdown:

• λεπτά = minutes
• ομιλίας = of speech / of talking

So λεπτά ομιλίας is a common kind of telecom phrase meaning the minutes you can use for voice calls.

Ομιλίας is the genitive singular of η ομιλία.

• η ομιλία = speech, talk, conversation
• της ομιλίας = of the speech / of talking

In λεπτά ομιλίας, the genitive shows a relationship similar to English of:

• minutes of talking
• more naturally: talk minutes

So the genitive here tells you what kind of minutes they are.

Because Greek often leaves out the article in a genitive phrase when the meaning is general or classificatory.

So:

• λεπτά ομιλίας = talk minutes / calling minutes
  not
• λεπτά της ομιλίας = the minutes of the speech/conversation

If you added της, it would sound much more specific, as if you meant a particular speech or conversation. Here the meaning is general, so ομιλίας appears without an article.

Είναι means both is and are in the present tense.

Examples:

• Το πρόγραμμα είναι καλό. = The plan is good.
• Τα λεπτά είναι αρκετά. = The minutes are enough.

So Greek does not change this verb form between singular and plural in the third person present. The same form είναι is used for both.

Στο is a contraction of:

• σε = in / at / to
• το = the

So:

• σε + το = στο

This is very common in Greek.

Examples:

• στο σπίτι = in the house / at the house
• στο πρόγραμμα = in the plan / on the plan

In this sentence, είναι στο πρόγραμμα literally means are in the plan, but idiomatically it means are included in the plan.

Modern Greek uses the accusative after σε.

So:

• το πρόγραμμα = the plan/program
• στο πρόγραμμα = in the plan

Even though English might make you think of an older dative-like idea, in Modern Greek the noun after σε is normally in the accusative.

It means something like contract plan.

Breakdown:

• πρόγραμμα = plan / program
• συμβολαίου = of contract

Literally, it is plan of contract, but natural English is contract plan.

This is another genitive relationship, just like λεπτά ομιλίας:

• πρόγραμμα συμβολαίου = plan of contract
• natural English: contract plan

In mobile-phone language, this usually refers to a plan tied to a contract, as opposed to prepaid service.

Because it depends on πρόγραμμα and describes what kind of plan it is.

• το συμβόλαιο = the contract
• του συμβολαίου = of the contract
• πρόγραμμα συμβολαίου = contract plan

Greek very often uses the genitive where English uses a noun modifier:

• σύμβαση εργασίας = employment contract
• κάρτα μνήμης = memory card
• πρόγραμμα συμβολαίου = contract plan

So συμβολαίου is genitive because it means of contract.

For the same general reason as with ομιλίας: the genitive noun is being used to classify the first noun, not to refer to one specific contract.

So:

• πρόγραμμα συμβολαίου = a contract plan / contract-plan type
• πρόγραμμα του συμβολαίου = the plan of the contract

The second version sounds much more specific, as if you are talking about one particular contract. In your sentence, the meaning is more general, so the article is omitted.

Yes. Literally, είναι στο πρόγραμμα συμβολαίου means are in the contract plan, but in this context Greek speakers naturally understand it as:

• are included in the contract plan
• come with the contract plan

Greek often uses είμαι + σε/στο in places where English prefers included in, part of, or available on.

Yes, Greek word order is more flexible than English, although not completely free.

The sentence as given is neutral and clear:

• Τα απεριόριστα λεπτά ομιλίας είναι στο πρόγραμμα συμβολαίου.

You could also move things around for emphasis, for example:

• Στο πρόγραμμα συμβολαίου είναι τα απεριόριστα λεπτά ομιλίας.

That sounds more marked, as if emphasizing where the unlimited minutes are included. But the original order is the most straightforward for a learner.

Here, plan is better.

Although πρόγραμμα can mean program/programme in many contexts, in mobile-phone and service contexts it often means:

• plan
• tariff plan
• package

So in this sentence, πρόγραμμα συμβολαίου is best understood as contract plan, not contract program.

A rough pronunciation guide is:

TA a-pe-ri-OR-ee-sta le-PTA o-mi-LEE-as EE-ne sto PRO-gram-ma sym-vo-LAY-ou

A few useful notes:

• αι is usually pronounced like e in modern Greek.
• οι and η/ι/υ are all pronounced like ee.
• μπ, ντ, γκ can have special sounds, but none of those affect this sentence much.
• Stress matters a lot in Greek, so notice:
  • απεριόριστα
  • ομιλίας
  • πρόγραμμα
  • συμβολαίου

It breaks down like this:

• Τα απεριόριστα λεπτά ομιλίας = subject
• είναι = verb
• στο πρόγραμμα συμβολαίου = prepositional phrase showing where/in what

So the structure is basically:

[Subject] + [to be] + [in the contract plan]

More literally:

• The unlimited talk minutes are in the contract plan

More naturally in English:

• Unlimited talk minutes are included in the contract plan.