Todo animal de estimação adotado precisa de cuidado.

Because todo + singular noun usually means every/each.

So:

• Todo animal de estimação adotado precisa de cuidado. = Every adopted pet needs care.

If you say todos os animais, that means all the animals and refers to a plural set:

• Todos os animais de estimação adotados precisam de cuidado(s). = All adopted pets need care.

A very useful contrast is:

• todo animal = every animal
• todo o animal = the whole animal
• todos os animais = all the animals

Animal de estimação is the standard expression for pet.

Literally, it is something like:

• animal = animal
• de estimação = kept with affection / as a pet

So animal de estimação functions as one unit meaning pet animal or simply pet.

In everyday Brazilian Portuguese, people also very often say pet, especially in informal or commercial contexts. But animal de estimação is a very natural and standard phrase.

In Portuguese, adjectives usually come after the noun.

So:

• animal adotado = adopted animal

Here, adotado describes animal de estimação, so it comes after the whole noun phrase:

• animal de estimação adotado = adopted pet

Also, adotado is the past participle of adotar and is being used like an adjective here.

Adotado agrees with the noun it describes in gender and number.

Here the head noun is animal, which is:

• masculine
• singular

So the form is adotado.

Compare:

• o animal adotado = the adopted animal
• a gata adotada = the adopted female cat
• os animais adotados = the adopted animals
• as gatas adotadas = the adopted female cats

Even though estimação is feminine, that does not control the agreement. The adjective agrees with animal, not with estimação.

Because the verb precisar is commonly used with de when it means to need.

So:

• precisar de algo = to need something
• precisar de cuidado = to need care

Examples:

• Eu preciso de ajuda. = I need help.
• Ela precisa de descanso. = She needs rest.

In everyday Brazilian Portuguese, you may sometimes hear precisar without de, especially in speech, but precisar de is the standard and safest form for learners.

Both can work, but they are slightly different in feel.

• precisa de cuidado = needs care
• precisa de cuidados = needs care / needs attention / needs proper care

The singular cuidado can express care as a general idea, like an uncountable noun in English.

The plural cuidados is also very common and can sound a bit more natural in many contexts because it suggests acts of care, attention, and maintenance.

So this sentence is grammatical, but many speakers might also naturally say:

• Todo animal de estimação adotado precisa de cuidados.

Portuguese often omits the article when speaking in a general sense.

So:

• precisa de cuidado = needs care
• precisa de atenção = needs attention
• precisa de amor = needs love

If you add an article, the meaning can become more specific:

• precisa do cuidado de um veterinário = needs the care of a veterinarian

Without the article, cuidado is more general and abstract.

No. The original order is the natural one.

• animal de estimação is a fixed expression meaning pet
• adotado then describes that whole phrase

So:

• todo animal de estimação adotado = every adopted pet

If you say animal adotado de estimação, it sounds awkward and unnatural, because it breaks up the expression animal de estimação.

Yes, absolutely. That is very natural in Brazilian Portuguese.

• Todo pet adotado precisa de cuidados.

This is shorter and very common in everyday speech.

The difference is mostly style:

• animal de estimação = a bit more formal or neutral
• pet = very common, modern, conversational

There are two main possibilities, depending on meaning.

If you want every in a plural-looking English translation, Portuguese still usually uses the singular:

• Todo animal de estimação adotado precisa de cuidado(s). = Every adopted pet needs care.

If you want all adopted pets, then use plural:

• Todos os animais de estimação adotados precisam de cuidado(s). = All adopted pets need care.

Notice the changes:

• todo → todos os
• adotado → adotados
• precisa → precisam

Yes. This sentence is making a general statement.

Portuguese often uses the singular for this kind of broad truth:

• Todo aluno precisa estudar. = Every student needs to study.
• Toda criança precisa de atenção. = Every child needs attention.

So Todo animal de estimação adotado precisa de cuidado means this is true as a general rule for adopted pets.

In Brazilian Portuguese, estimação ends with a nasal sound: -ão.

A rough pronunciation guide is:

• estimação ≈ es-chee-ma-SOWN (very rough approximation)

A few useful points:

• ti before a vowel in many Brazilian accents sounds like chee
• ção has a nasal ending, not a full English ow
• de estimação is usually said smoothly together in connected speech

You do not need a perfect English-style spelling of the sound; the most important thing is learning that -ão is nasal and very common in Portuguese words.