O gato dorme embaixo da cama.

In Portuguese, definite articles are used more often than in English. So o gato means the cat, and it sounds very natural here.

You can sometimes omit the article, but that usually changes the meaning:

• O gato dorme... = The cat is sleeping / sleeps...
• Gato dorme muito. = Cats sleep a lot or A cat sleeps a lot in a more general sense

So in this sentence, o gato refers to a specific cat.

Dormir is the infinitive, meaning to sleep.

In the sentence, the verb has to match the subject:

• eu durmo = I sleep
• você / ele / ela dorme = you / he / she sleeps

Since o gato is third-person singular (it / he), the correct form is dorme.

So:

• O gato dorme. = The cat sleeps / is sleeping.

Portuguese often uses the simple present in places where English might prefer either:

• sleeps for a general fact, or
• is sleeping for something happening right now

So O gato dorme embaixo da cama can mean:

• The cat sleeps under the bed if you mean that is its habit, or
• The cat is sleeping under the bed if the context shows it is happening now

If you want to make the ongoing action extra clear, Brazilian Portuguese often uses:

• O gato está dormindo embaixo da cama.

Da is a contraction of:

• de = of / from
• a = the

So:

• de + a = da

In this sentence, da cama literally means of the bed, but in natural English the whole phrase becomes under the bed.

This happens because embaixo normally goes with de:

• embaixo de algo = under something

So:

• embaixo da cama = under the bed

Because embaixo normally needs the preposition de:

• embaixo de + noun

Then de combines with the article:

• de + a cama → da cama

So the structure is:

• embaixo de a cama → embaixo da cama

You cannot normally say:

• embaixo a cama
• embaixo cama

Those sound ungrammatical in standard Portuguese.

Yes, here embaixo is written as one word and means under / underneath / below.

This is the normal spelling in this expression:

• embaixo da cama = under the bed

You may also see em baixo as two words in other contexts, but that is a different structure and usually means something more like in a low place or down low, depending on context.

For this sentence, embaixo is definitely the correct form.

Yes. In Brazilian Portuguese, embaixo da cama and debaixo da cama are both very common and usually mean the same thing: under the bed.

So these are both natural:

• O gato dorme embaixo da cama.
• O gato dorme debaixo da cama.

In most everyday situations, the difference is minimal or nonexistent.

Yes. Cama is a feminine noun, so its article is a:

• a cama = the bed

Because embaixo takes de, you get:

• de + a cama = da cama

If the noun were masculine, you would get do instead:

• de + o = do

Example:

• embaixo do carro = under the car

The normal word order is:

subject + verb + prepositional phrase

So:

• O gato = subject
• dorme = verb
• embaixo da cama = location

This is the most neutral, natural order:

• O gato dorme embaixo da cama.

You can move things around for emphasis, for example:

• Embaixo da cama, o gato dorme.

But that sounds more marked or literary. For a learner, the original order is the safest and most natural choice.

A rough Brazilian Portuguese pronunciation is:

oo GAH-too DOR-mee em-BAI-shoo da KAH-ma

A few helpful notes:

• gato: the a is open, and the t is a clear t
• dorme: stress is on dor
• embaixo: the x here sounds like sh
• cama: stress is on the first syllable, KA

In natural speech, it may sound smoother and more connected than the careful word-by-word version.

If you are talking about a specific animal, yes, using the article is very common and usually expected:

• O gato dorme. = The cat is sleeping.

If you are speaking more generally, you might leave it out:

• Gato é independente. = Cats are independent / The cat as a species is independent

So in this sentence, o is there because it refers to a particular cat, not cats in general.