Αν έχουμε καλή συνεννόηση, η επόμενη σύσκεψη θα τελειώσει γρήγορα και χωρίς ένταση.

Because after αν in a normal if clause, Greek does not use θα.

A very common pattern is:

• αν + present
• main clause with θα

So:

• Αν έχουμε καλή συνεννόηση, ... θα τελειώσει ...

works like English:

• If we have good coordination/understanding, ... will finish ...

Using Αν θα έχουμε here would be ungrammatical.

Συνεννόηση means something like good communication, coordination, mutual understanding, being on the same page.

It is not quite the same as understanding in the sense of intellectual comprehension. For that, Greek often uses κατανόηση.

So καλή συνεννόηση is a very natural Greek expression for people working together smoothly and understanding each other well.

Καλή agrees with συνεννόηση.

• συνεννόηση is feminine singular
• so the adjective must also be feminine singular: καλή

In this sentence, συνεννόηση is the direct object of έχουμε, so it is in the accusative. But with many feminine nouns and adjectives, the nominative and accusative look the same in writing:

• καλή συνεννόηση

So even though it is the object, the form still looks like καλή.

Because the phrase is indefinite and general.

Greek often leaves out the article in expressions like:

• έχουμε καλή συνεννόηση
• έχουμε χρόνο
• έχει υπομονή

Here the meaning is general: if we have good mutual understanding / good communication.

If you added an article, it would sound more specific, as if you were talking about a particular previously known understanding, which is not the idea here.

Because this refers to a specific meeting: the next meeting.

Greek uses the definite article very often, and with words like επόμενος it is especially natural when you mean a particular identifiable thing:

• η επόμενη σύσκεψη = the next meeting

Also, η, επόμενη, and σύσκεψη all agree:

• feminine
• singular
• nominative

because this is the subject of the sentence.

Both can be translated as meeting, but they are not exactly the same.

• σύσκεψη usually sounds more formal, often a work, business, or official meeting
• συνάντηση is broader and can mean almost any meeting, formal or informal

So η επόμενη σύσκεψη suggests something like a planned discussion, conference, or work meeting rather than just any meeting-up.

This is a question of aspect, which is very important in Greek.

• θα τελειώσει presents the action as a whole, completed event: will end / will finish
• θα τελειώνει is imperfective and would suggest something more like will be ending or an ongoing/repeated idea

Here the speaker is talking about one future meeting reaching its end, so θα τελειώσει is the natural choice.

Yes. In Greek, τελειώνω can be used both:

• transitively: finish something
• intransitively: come to an end

So:

• Η σύσκεψη θα τελειώσει

is perfectly natural and means The meeting will end.

Greek does this very often with verbs that in English may need slightly different wording.

Because γρήγορα is an adverb, meaning quickly, and it modifies the verb θα τελειώσει.

• γρήγορα = quickly
• γρήγορη = quick, feminine adjective

Compare:

• Η σύσκεψη θα τελειώσει γρήγορα = The meeting will finish quickly
• Η σύσκεψη είναι γρήγορη = The meeting is quick

So here Greek needs the adverb, not the adjective.

After χωρίς, Greek often uses an abstract noun without an article when the meaning is general.

So:

• χωρίς ένταση = without tension / without conflict / without strain

This means the meeting will end calmly, without friction or raised tempers.

If you said χωρίς την ένταση, that would point to a specific tension already known from the context.

Here ένταση does not mean intensity in a neutral technical sense. It means something more like:

• tension
• strain
• friction
• heated atmosphere

So χωρίς ένταση suggests that the meeting will finish peacefully, without arguments or stress between the people involved.

Yes. Greek word order is fairly flexible, and this sentence uses a natural, neutral order.

You could also say:

• Η επόμενη σύσκεψη θα τελειώσει γρήγορα και χωρίς ένταση, αν έχουμε καλή συνεννόηση.

That still means basically the same thing. The difference is mostly one of emphasis and flow, not core grammar.

Because the sentence begins with a subordinate if clause:

• Αν έχουμε καλή συνεννόηση,

and then moves to the main clause:

• η επόμενη σύσκεψη θα τελειώσει γρήγορα και χωρίς ένταση.

In standard Greek punctuation, a fronted conditional clause is normally separated from the main clause with a comma.