Learn Hardcore Portuguese (Portugal): Ao terminar o exame, eu descanso um pouco.

So Ao terminar o exame = When I finish the exam / Upon finishing the exam. It’s a very common, quite natural way in European Portuguese to talk about what happens at the moment another action is completed.

Could I say Quando terminar o exame, eu descanso um pouco instead? Is there any difference?

Yes, you can say:

Quando terminar o exame, eu descanso um pouco.

Differences:

Ao terminar is a bit more compact and often feels slightly more formal or written, but it’s perfectly normal in speech.
Quando terminar is more neutral and very common.

In many contexts they are interchangeable. Ao terminar subtly focuses on the moment of finishing, while quando terminar is just when I finish, without that extra “upon/at the moment of” nuance.

Who is the subject of terminar in Ao terminar o exame? Why isn’t eu repeated?

The understood subject of terminar is eu, the same subject as in the main clause:

Ao terminar o exame, eu descanso um pouco.
→ When I finish the exam, I rest a bit.

In Portuguese, when you have ao + infinitive like this, the subject is normally the same as the subject of the main clause, so it doesn’t need to be repeated.

If you wanted a different subject, you’d normally make it explicit, for example:

Ao terminar o exame, os alunos saem da sala.
(When they finish the exam, the students leave the room.)

Why is there a comma after Ao terminar o exame?

Because the sentence starts with a dependent (subordinate) clause:

Ao terminar o exame, → time clause
eu descanso um pouco. → main clause

In Portuguese, when a subordinate clause comes before the main clause, it is typically separated by a comma. If you reverse the order, you normally drop the comma:

Eu descanso um pouco ao terminar o exame. (no comma)

Why is it descanso and not descansar here?

Descanso is the present indicative, 1st person singular of descansar:

eu descanso = I rest.

So:

eu descanso um pouco = I rest a bit.

Descansar (the infinitive) would be used in other structures, for example:

Eu vou descansar um pouco. (I am going to rest a bit.)
Gosto de descansar. (I like to rest.)

Also note: descanso can be a noun (o descanso = the rest), but in this sentence it’s clearly the verb form because it follows eu and takes an object/adverb (um pouco).

Why is the present tense used (eu descanso) if this is about the future (after I finish)?

Portuguese often uses the present tense to talk about:

habitual actions
future actions in time clauses, or in instructions/schedules

Here, Ao terminar o exame, eu descanso um pouco can be understood as:

a habit/routine: Whenever I finish an exam, I rest a bit.
or a planned future step in an instruction sequence: When I finish the exam, I (then) rest a bit.

If you want to make it clearly about a specific future plan, you can say:

Ao terminar o exame, vou descansar um pouco.
(When I finish the exam, I’m going to rest a bit.)

Is the subject pronoun eu necessary here?

No, it’s not strictly necessary. European Portuguese often drops subject pronouns because the verb ending already shows the person:

Ao terminar o exame, descanso um pouco.

This is perfectly natural in European Portuguese.
Including eu adds a little emphasis (for example, contrasting with other people), or it can be used just for clarity or style.

Why is it o exame and not meu exame or just exame without an article?

In European Portuguese:

The definite article is used very frequently with concrete nouns, even when English would omit it.
O exame here means the exam (we are talking about / that I’m taking). The context usually makes clear whose exam it is.

Alternatives:

meu exame = my exam – possible, but it sounds more marked, as if you are explicitly contrasting your exam with someone else’s, or you really want to stress possession.
zero article (∅ exame) would sound unnatural here; European Portuguese almost always uses an article with exame in this kind of sentence.

So o exame is the most natural form in European Portuguese in this context.

Could I say Depois de terminar o exame, eu descanso um pouco? How is that different from Ao terminar o exame?

Yes, you can say:

Depois de terminar o exame, eu descanso um pouco.

Differences:

Ao terminar o exame = when / upon finishing the exam, focusing on the moment of finishing.
Depois de terminar o exame = after finishing the exam, focusing more on what happens later, not necessarily immediately.

In many real situations they overlap, but ao terminar often suggests something that follows right away, whereas depois de can feel a bit more open in time.

Is the position of um pouco fixed? Could I put it somewhere else?

The normal position is after the verb:

eu descanso um pouco.

Other possibilities:

Eu um pouco descanso. → sounds unnatural.
Eu descanso um pouco depois. → okay, but then depois adds “later”.

So for the simple idea “I rest a bit”, descanso um pouco is the natural, standard order.

In European Portuguese you might also hear synonyms like:

descanso um bocadinho (very common, a bit/informal)
descanso um bocado (also common, a bit/some)

Would Brazilians say this sentence the same way?

They can understand and use it, but they might prefer slightly different wording:

Ao terminar a prova, eu descanso um pouco.
(In Brazil, prova is more common than exame in the school/college context.)

Also:

In Brazilian Portuguese, eu is used more often; dropping it is still possible but less frequent in everyday speech.
Brazilians might more often say:
Quando terminar a prova, eu vou descansar um pouco.
using quando and vou descansar to talk about a specific future event.

So your original sentence is perfectly correct Portuguese; it just sounds a bit more naturally European in vocabulary and style.

How would I say the same idea in a more informal or very natural European Portuguese way?

Your sentence is already natural, but some slightly more colloquial options in European Portuguese are:

Quando acabar o exame, descanso um bocadinho.
Assim que acabar o exame, descanso um bocado.

Changes:

acabar instead of terminar (very common in speech)
um bocadinho / um bocado instead of um pouco (more colloquial)
subject eu omitted, as is usual in speech.