Το πρόγραμμα προβών τελειώνει με τη γενική πρόβα.

Because το πρόγραμμα προβών means the schedule of rehearsals or the rehearsal schedule.

In Greek, when one noun is defined by another noun, the second noun is often put in the genitive:

• το πρόγραμμα = the schedule / the program
• των προβών = of the rehearsals

In this sentence, των is omitted because Greek often leaves out the article in this kind of expression when the meaning is still clear:

• το πρόγραμμα προβών = literally the schedule of rehearsals

So:

• πρόβα = rehearsal
• προβών = of rehearsals

This is a very common Greek structure:

• το κέντρο της πόλης = the center of the city
• το πρόγραμμα μαθημάτων = the class schedule / schedule of classes

The dictionary form is η πρόβα.

Here are the relevant forms:

• η πρόβα = the rehearsal
• οι πρόβες = the rehearsals
• των προβών = of the rehearsals

So προβών is the genitive plural form of πρόβα.

Greek often uses the present tense for things that are generally true, scheduled, or part of a plan.

So Το πρόγραμμα προβών τελειώνει με τη γενική πρόβα means something like:

• The rehearsal schedule ends with the dress rehearsal
• The rehearsal program ends with the final rehearsal

Even though in English we might also use the present here, learners sometimes expect a future form. But Greek present tense works very naturally for schedules, plans, and descriptions of how something is structured.

τελειώνει is the 3rd person singular of τελειώνω:

• τελειώνω = I finish / I end
• τελειώνει = it finishes / it ends

Since το πρόγραμμα is singular, the verb is singular too.

Here με means with, in the sense of ending with something.

So:

• τελειώνει με... = ends with...

This is a very natural Greek expression:

• Η ταινία τελειώνει με έναν γάμο. = The movie ends with a wedding.
• Το μάθημα τελειώνει με μια άσκηση. = The lesson ends with an exercise.

In your sentence:

• με τη γενική πρόβα = with the dress rehearsal / final rehearsal

Both are related to the feminine accusative singular article:

• την

Before some consonants, especially in everyday modern Greek, the final -ν is often dropped:

• την πρόβα → τη πρόβα

So με τη γενική πρόβα is a normal form.

Very roughly:

• την is the full form
• τη is the shortened form often used before many consonants

You will see both in writing depending on style, spelling conventions, and the sound that follows.

Because it has to agree with πρόβα.

πρόβα is:

• feminine
• singular
• accusative here (because it follows με)

So the adjective γενικός changes to match it:

• masculine: γενικός
• feminine: γενική
• neuter: γενικό

Thus:

• η γενική πρόβα = the dress rehearsal / the general rehearsal
• με τη γενική πρόβα = with the dress rehearsal

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

Yes. Literally, γενική πρόβα means general rehearsal.

But in natural English, this is usually translated as:

• dress rehearsal
• sometimes final rehearsal, depending on context

So a learner should know both:

• literal meaning: general rehearsal
• natural translation: dress rehearsal

Because Greek often leaves out the article in this kind of noun + genitive expression.

Compare:

• το πρόγραμμα των προβών = the schedule of the rehearsals
• το πρόγραμμα προβών = the rehearsal schedule / schedule of rehearsals

Both are possible, but the version without the article is very common and often sounds more compact or general.

This happens a lot in Greek:

• πρόγραμμα μαθημάτων = class schedule
• αίθουσα συνεδριάσεων = meeting room
• στάση λεωφορείου = bus stop

So πρόγραμμα προβών is a standard kind of structure.

Yes, Greek word order is more flexible than English word order.

The neutral, straightforward order here is:

• Το πρόγραμμα προβών τελειώνει με τη γενική πρόβα.

But other orders are possible for emphasis, for example:

• Με τη γενική πρόβα τελειώνει το πρόγραμμα προβών.

That version puts emphasis on with the dress rehearsal.

Even though Greek allows more flexibility, the original sentence is the most neutral and natural way to say it in most contexts.

They are two forms of the same noun, but they play different roles.

• πρόβα = rehearsal
  Here it appears in τη γενική πρόβα, meaning the dress rehearsal. This is singular.

• προβών = of rehearsals
  Here it appears in το πρόγραμμα προβών, meaning the schedule of rehearsals. This is genitive plural.

So the sentence contains:

• one specific rehearsal: the dress rehearsal
• the whole set of rehearsals: the rehearsals

That is why Greek uses two different forms of the same noun.

Often yes, but not always in exactly the same way.

το πρόγραμμα can mean:

• program
• schedule
• timetable
• plan

In this sentence, schedule is usually the most natural translation:

• Το πρόγραμμα προβών = the rehearsal schedule

So even though the Greek word looks like English program, the best English meaning depends on context. Here it refers to the sequence or plan of rehearsals.