Kad izađemo iz kina, ići ćemo na kavu.

Because Croatian often uses the present tense in a time clause after kad when talking about a future event.

Here, izađemo is the present-tense form of the verb izaći. In this sentence, it means something like:

• when we come out
• or more exactly, when we have come out / once we come out

So even though the whole situation is in the future, Croatian does not normally use a future form after kad here.

This is actually not so different from English, which also says:

• When we come out of the cinema, we’ll go for coffee.

not:

• When we will come out...

This is about aspect, which is very important in Croatian.

• izaći = perfective verb
• izlaziti = imperfective verb

In this sentence, the speaker means one completed action:

• first, we come out of the cinema
• then, we go for coffee

Because the action of coming out is seen as completed before the next action, Croatian uses the perfective verb izaći, giving izađemo.

If you used izlazimo, it would sound more like an ongoing, repeated, or habitual action, which does not fit as well here.

Yes. ići ćemo is the future tense of ići (to go).

Croatian future tense is formed with:

• the infinitive of the main verb
• plus forms of htjeti used as an auxiliary

So:

• ići ćemo = we will go

Here:

• ići = to go
• ćemo = we will

So the main clause is in the future:

• ići ćemo na kavu = we’ll go for coffee

Because ćemo is a clitic in Croatian, and clitics usually cannot stand at the very beginning of a clause.

So in this sentence, Croatian naturally says:

• ići ćemo na kavu

not:

• ćemo ići na kavu

If another word came first, then ćemo could follow that first element, for example:

• Sutra ćemo ići na kavu. = Tomorrow we’ll go for coffee.

So the issue is mostly word order and clitic placement.

Because Croatian often drops subject pronouns when they are already clear from the verb form.

In this sentence, we is understood from:

• izađemo = we come out
• ćemo = we will

So there is no need to say mi unless you want emphasis or contrast.

For example:

• Kad izađemo iz kina, ići ćemo na kavu. = neutral
• Kad mi izađemo iz kina, ići ćemo na kavu. = more emphatic, like when we come out...

This is very normal in Croatian.

Because the preposition iz requires the genitive case.

The noun is:

• kino = cinema

Its genitive singular form is:

• kina

So:

• iz kina = out of the cinema / from the cinema

This is a common pattern:

• iz kuće = out of the house
• iz grada = out of the city
• iz škole = out of school

So the ending changes because of the case required by iz.

Because na here expresses movement toward a goal/purpose, so it takes the accusative case.

The noun is:

• kava = coffee

Its accusative singular is:

• kavu

So:

• na kavu = literally for/to coffee
• idiomatically for coffee

This is a very common Croatian expression:

• ići na kavu = to go for coffee

It often means not just drinking coffee, but also meeting socially.

Not necessarily in a strict mathematical sense.

In Croatian, ići na kavu is a very common idiomatic expression meaning:

• to go for coffee
• to go out for a coffee
• sometimes even to meet up and chat over coffee

So na kavu can refer to:

• having a coffee
• going to a café
• a social coffee outing

Even if someone ends up drinking something else, the phrase can still be used because it often refers to the social event, not only the drink itself.

Yes, in this sentence they mean the same thing: when.

• kad = shorter, very common in everyday speech
• kada = slightly fuller, sometimes a bit more formal or careful in style

So both are possible:

• Kad izađemo iz kina, ići ćemo na kavu.
• Kada izađemo iz kina, ići ćemo na kavu.

The meaning does not really change here.

Because Kad izađemo iz kina is a subordinate time clause placed before the main clause.

So the structure is:

• Kad izađemo iz kina = subordinate clause
• ići ćemo na kavu = main clause

Croatian separates that opening clause with a comma:

• Kad izađemo iz kina, ići ćemo na kavu.

This is similar to English punctuation in:

• When we come out of the cinema, we’ll go for coffee.

Yes. Croatian word order is fairly flexible.

You could also say:

• Ići ćemo na kavu kad izađemo iz kina.

This has the same basic meaning. The difference is mostly focus:

• Kad izađemo iz kina, ići ćemo na kavu.
  Emphasizes the time/condition first
• Ići ćemo na kavu kad izađemo iz kina.
  Starts with the main plan: we’ll go for coffee

Both are natural.