Learn Hardcore Croatian: Poslije utakmice polako izlazimo iz dvorane. - After the match we slowly leave the hall.

Both poslije and nakon take the genitive case (utakmice).
nakon is slightly more formal or neutral; poslije is very common in everyday speech.
In most everyday contexts, you can freely swap them without changing the meaning.

Why is there no word for we in the Croatian sentence? Where is the subject?

Croatian normally drops subject pronouns when they’re clear from the verb ending. It is a “pro‑drop” language.

The verb izlazimo ends in -mo, which marks 1st person plural (we).
So izlazimo already means we are going out.

You could say Mi polako izlazimo iz dvorane, but:

Mi is usually added only for emphasis or contrast, like We (as opposed to someone else) are the ones who are slowly leaving the hall.

Why is it iz dvorane and not something like iz dvorana or iz dvoranu?

The preposition iz (out of, from inside) also takes the genitive case.

Nominative: dvorana (hall)
Genitive singular: dvorane

So:

✅ iz dvorane = out of the hall
❌ iz dvoranu – wrong case (accusative).
iz dvorana would be genitive plural, meaning out of (several) halls, which doesn’t fit this context.

Here, we’re talking about one specific hall, so iz dvorane is correct.

What exactly does dvorana mean in this sentence?

Dvorana is a hall or large indoor space, and in a sports context it usually refers to a sports hall / gym / arena.

So in this sentence, dvorana is best understood as the sports hall or the indoor arena, not a regular room:

iz dvorane ≈ out of the (sports) hall / gym.

What does polako mean here? Does it mean slowly, quietly, or something else?

Polako literally means slowly.

In this context:

polako izlazimo = we are leaving slowly / we are slowly going out.

Depending on the situation, polako can also imply:

unhurriedly, calmly, gently.

It does not mean “quietly” by default (that would usually be tiho), although moving slowly and calmly can sometimes imply being quiet in context.

Can I change the position of polako? For example, can I say Polako izlazimo iz dvorane?

Yes. Croatian word order is relatively flexible, especially for adverbs like polako.

All of these are grammatically fine and natural, with only small differences in emphasis:

Poslije utakmice polako izlazimo iz dvorane.
Poslije utakmice izlazimo polako iz dvorane.
Poslije utakmice izlazimo iz dvorane polako.
Polako izlazimo iz dvorane poslije utakmice. (less common, more stylized)

Neutral, typical versions for this meaning would be:

Poslije utakmice polako izlazimo iz dvorane.
Poslije utakmice izlazimo polako iz dvorane.

Why is the verb izlazimo in the present tense if the action happens after the match (in the future)?

Croatian often uses the present tense for:

Regular / habitual actions:
- Poslije svake utakmice polako izlazimo iz dvorane.
  = After every match, we (always) slowly leave the hall.
Scheduled future events (especially with time expressions):
- Poslije utakmice polako izlazimo iz dvorane.
  can mean: Once the match ends, our plan is that we (will) leave the hall slowly.

If you want to stress a one-time future action, you can also use the future tense:

Poslije utakmice ćemo polako izaći iz dvorane. = After the match, we will slowly go out of the hall.

What is the difference between izlazimo and izađemo / izaći?

This is about aspect:

izlaziti (imperfective) → izlazimo
Focuses on the process of going out, or a repeated/habitual action.
izaći (perfective) → izađemo, ćemo izaći
Focuses on the completion of the action (the result: we end up outside).

In your sentence:

Poslije utakmice polako izlazimo iz dvorane.
= We are (in the process of) slowly going out / we usually leave slowly.

If you say:

Poslije utakmice ćemo polako izaći iz dvorane.
= We will (eventually, once finished) go out slowly; it highlights the finished event in the future.

Why is it iz dvorane and not od dvorane or sa dvorane?

Different prepositions express different types of “from”:

iz
- genitive = from the inside of something
  - iz dvorane = out of the hall (from inside it)
od
- genitive = from someone/something (origin, distance, possession)
  - daleko od dvorane = far from the hall
sa
- genitive = from a surface or an open area, or “from” in some idioms
  - sa stola = from (off) the table
  - sa igrališta = from the (open) playing field

Here we are leaving the interior of a building, so iz dvorane is correct.

Could I say Poslije utakmice polako izlazimo iz sale instead of iz dvorane?

Yes, but there is a nuance:

dvorana – more strongly suggests a larger hall, often a sports hall or arena.
sala – can also mean hall / large room (like a function room, concert hall, etc.), and in some regions it’s more common in everyday speech.

In many situations they would both be understood, but:

At a sports event, iz dvorane feels more standard and precise.
In some dialects/regions, sala is very common in everyday talk.

Is poslije utakmice the same as po utakmici?

They are close, but not identical in use:

poslije utakmice (genitive) = after the match
→ very common and fully standard.
po utakmici (locative) can also mean after the match, especially in some dialects and in more colloquial speech, but it is:
- less neutral/standard in this time-meaning,
- more regionally coloured.

For clear, standard Croatian, poslije utakmice or nakon utakmice is preferred in this sense.