A seguradora indemnizou o cliente.

They are the definite articles:

• a = feminine singular the
• o = masculine singular the

So:

• a seguradora = the insurer
• o cliente = the client

Portuguese often uses definite articles in places where English also uses the, and sometimes even where English would leave it out. Here, both nouns are presented as specific.

Because seguradora is a feminine noun. In Portuguese, nouns have grammatical gender, and the article must match:

• a seguradora
• o segurador

In practice, seguradora is the usual word for an insurance company, so the feminine article is normal here.

Indemnizou is the pretérito perfeito simples (simple preterite), 3rd person singular, of indemnizar.

It refers to a completed action in the past.

Formation:

• infinitive: indemnizar
• stem: indemniz-
• ending for ele/ela/você in this tense: -ou

So indemnizou means he/she/it compensated / indemnified.

Because indemnizar takes a direct object. You indemnify someone, so Portuguese says:

• indemnizar alguém

That means o cliente is the direct object, with no preposition.

Compare:

• A seguradora indemnizou o cliente.
• A seguradora telefonou ao cliente.

In the second example, telefonar normally needs a, so you get ao cliente. But indemnizar does not.

No. Cliente is a common-gender noun: the noun form stays the same, and the article changes.

• o cliente = a male client
• a cliente = a female client

So in this sentence, o cliente refers to a male client, or to a client presented with masculine agreement.

Yes, especially in insurance, legal, and formal contexts. It sounds very natural in a sentence about an insurance company.

In more casual speech, people might also say:

• pagar uma indemnização ao cliente
• compensar o cliente

But with seguradora as the subject, indemnizou is exactly the kind of verb you would expect.

In European Portuguese, indemnizou is pronounced with the stress on the last syllable: -zou. A rough English-friendly approximation is in-duhm-nee-ZOH, though the unstressed vowels are reduced more in real European Portuguese speech.

A useful spelling note:

• European Portuguese: indemnizar / indemnizou
• Brazilian Portuguese: usually indenizar / indenizou

So this is one of those words where Portugal and Brazil often spell it differently.

Yes. Since o cliente is a direct object, you can replace it with o:

• A seguradora indemnizou-o.

If it were a female client:

• A seguradora indemnizou-a.

In European Portuguese, in an affirmative main clause, the object pronoun usually comes after the verb and is attached with a hyphen, as in indemnizou-o.

Yes:

• O cliente foi indemnizado pela seguradora.

This means the same thing, but the focus shifts from the insurer to the client.

• A seguradora indemnizou o cliente. = active
• O cliente foi indemnizado pela seguradora. = passive

The passive version is especially common in formal, legal, and administrative Portuguese.