A cliente perguntou se o garçom poderia trazer outra fatia.

Because cliente is a common-gender noun in Portuguese. The noun itself stays the same, and the article shows the gender:

• o cliente = the male customer
• a cliente = the female customer

The same often happens with adjectives too:

• o cliente satisfeito
• a cliente satisfeita

So in this sentence, a tells you the customer is female.

A means the, while uma means a/an.

So:

• a cliente = a specific customer, probably already known in the context
• uma cliente = some female customer, not specifically identified yet

Using a cliente suggests the listener or reader is supposed to know which customer is being referred to.

Here, se means if or whether and introduces an indirect yes/no question.

So perguntou se o garçom poderia trazer outra fatia is structurally like:

• She asked if/whether the waiter could bring another slice

This se is not reflexive here. It is not the same as the se in verbs like chamar-se.

Poderia is the conditional form of poder.

In this sentence, it helps make the request sound more polite, softer, or less direct. It works a lot like English could in polite requests.

Compare:

• pode trazer = can bring / can you bring
• podia trazer = could bring / could you bring
• poderia trazer = could bring / would be able to bring, often a bit more polite or formal

So perguntou se o garçom poderia trazer... sounds natural for reporting a polite request.

Because after poder, the next verb normally stays in the infinitive.

So:

• poderia trazer
• pode trazer
• podia trazer

This is the same pattern as in English:

• could bring
• can bring

The first verb is conjugated, and the main action verb stays in its base form.

Because this se introduces an indirect question, not a conditional clause.

In other words, this sentence is not saying:

• If the waiter could bring another slice...

It is saying:

• She asked whether the waiter could bring another slice

That is why poderia is fine here.

Compare:

• A cliente perguntou se o garçom poderia trazer outra fatia.
  Indirect question: whether he could

• Se o garçom pudesse trazer outra fatia, seria ótimo.
  Conditional idea: if he could

In the second example, pudesse is subjunctive because the grammar is different.

Outra fatia means another slice.

• outra = another / other
• fatia = slice

Fatia is used for things that are cut into slices, such as cake, pie, pizza, ham, bread, and similar foods.

So the sentence suggests that the customer wanted one more slice of something.

Both can often be translated as another slice or one more slice, but there is a slight nuance:

• outra fatia = another slice
• mais uma fatia = one more slice

In many real situations, they are interchangeable.

A rough distinction:

• outra can feel a little more like an additional one
• mais uma can feel a little more explicitly numerical: one more

But in a restaurant context, both are very natural.

Portuguese often leaves out objects when the meaning is clear from context.

Here, the most obvious interpretation is that the waiter would bring the slice to the customer who asked. So lhe is not necessary.

A more explicit version would be:

• A cliente perguntou se o garçom poderia lhe trazer outra fatia.

In Brazilian Portuguese, especially in everyday speech, leaving the pronoun out is very common when there is no real confusion.

A little, yes — but usually not enough to cause a problem.

Grammatically, trazer outra fatia does not explicitly say to whom. But in context, the natural reading is that the waiter would bring it to the customer.

If you want to make it completely explicit, you could say:

• A cliente perguntou se o garçom poderia lhe trazer outra fatia.
• A cliente perguntou se o garçom poderia trazer outra fatia para ela.

Both remove any doubt.

Yes. Garçom normally refers to a male waiter.

For a female waiter, Brazilian Portuguese often uses garçonete.

So:

• o garçom = the male waiter
• a garçonete = the female waiter

In your sentence, o garçom clearly tells you the waiter is male.

Yes, absolutely.

That version is also natural and is a little more explicit:

• A cliente perguntou ao garçom se ele poderia trazer outra fatia.

It spells out the listener of the question with ao garçom and then uses ele inside the subordinate clause.

The original sentence is still correct and natural. Portuguese often allows this kind of omission when the reference is clear from context.