Quatro documentos estão prontos.

Because the subject is quatro documentos, which is plural. In Portuguese, the verb has to agree with the subject.

• documento = singular
• documentos = plural

So:

• O documento está pronto. = The document is ready.
• Os documentos estão prontos. = The documents are ready.

Since quatro documentos means four documents, the verb must be plural: estão.

Pronto is an adjective, and in Portuguese adjectives usually agree with the noun in gender and number.

Here, the noun is documentos:

• documento = masculine singular
• documentos = masculine plural

So the adjective must also be masculine plural:

• pronto = masculine singular
• prontos = masculine plural

Examples:

• O documento está pronto.
• Os documentos estão prontos.

Portuguese often uses estar for a state or condition, especially something seen as temporary or the result of a process.

Pronto means ready, so estar pronto is the normal expression for saying something is ready.

• O jantar está pronto. = Dinner is ready.
• Os documentos estão prontos. = The documents are ready.

Using ser here would sound unnatural in normal Portuguese.

With numbers, Portuguese often does not use the definite article unless you specifically mean a known or previously identified group.

So:

• Quatro documentos estão prontos. = Four documents are ready.
• Os quatro documentos estão prontos. = The four documents are ready.

The second version is more specific: it refers to those four documents.

Usually, no. After numbers greater than one, the noun is normally plural.

So:

• um documento
• dois documentos
• três documentos
• quatro documentos

This is different from English only in some special cases, because English also usually uses the plural after numbers. Here the pattern is very similar.

Yes. That means the four documents are ready.

Compare:

• Quatro documentos estão prontos. = Four documents are ready.
• Os quatro documentos estão prontos. = The four documents are ready.

Adding os makes the phrase more definite and specific.

Yes, but the most neutral order is:

• Quatro documentos estão prontos.

You may also hear:

• Estão prontos quatro documentos.

That version is possible, but it sounds more marked or stylistic. It may appear in formal writing, announcements, or when the speaker wants to emphasize the result/state first.

For everyday use, Quatro documentos estão prontos is the safest choice.

In Brazilian Portuguese, estão is pronounced roughly like eh-STOWng, but the ending is nasal, so it does not sound exactly like English ow.

A few points:

• Stress is on the last syllable: es-TÃO
• The ão sound is very common in Portuguese and is nasal
• The s in estão is usually pronounced like s in see

A rough learner-friendly approximation is:

• es-TOWN (but nasalized)

Numbers normally come before the noun in Portuguese, just like in English.

• quatro documentos = four documents
• duas casas = two houses
• dez livros = ten books

So quatro documentos is the normal order.

Usually in this sentence, prontos is not directly modifying the noun inside the noun phrase. It is part of the structure:

• documentos estão prontos

Here, prontos is a predicate adjective, linked to the noun by estar.

You can also use prontos directly with the noun in another structure:

• quatro documentos prontos = four ready documents

But that is a different construction from:

• Quatro documentos estão prontos.

Yes, if the context already makes it clear what is ready.

For example, if everyone knows you are talking about the documents, you can say:

• Estão prontos. = They are ready.

Portuguese often omits words that are understood from context. But if you are introducing the information clearly, saying Quatro documentos estão prontos is better.

Yes, it is completely natural.

It sounds like a normal statement you might hear in an office, school, legal setting, or any situation involving paperwork:

• Quatro documentos estão prontos.

A Brazilian speaker might also say:

• Já estão prontos quatro documentos.
• Os quatro documentos já estão prontos.

But your original sentence is correct and natural.