O gato está por baixo da mesa.

Because Portuguese usually uses estar for location.

• O gato está por baixo da mesa = the cat is under the table
• Ser (é) is normally used for identity, classification, or more permanent characteristics:
  • O gato é preto = the cat is black
  • É um gato = it is a cat

So for where something or someone is, estar is the normal choice.

Por baixo de means under, underneath, or below.

In this sentence:

• por baixo da mesa = under the table

It is a fixed expression made of several words:

• por
• baixo
• de

Learners often want to translate each word separately, but it is better to learn por baixo de as one unit meaning under/below.

Because in Portuguese, de + a normally contracts to da.

So:

• de + a mesa → da mesa

This kind of contraction is very common:

• de + o → do
• de + a → da
• em + a → na
• em + o → no

So por baixo da mesa is the correct contracted form.

O is the definite article, meaning the.

So:

• o gato = the cat
• um gato = a cat

Portuguese uses articles very often, sometimes more often than English. In this sentence, o gato refers to a specific cat, not just any cat.

Because baixo here is not acting like a normal adjective directly describing mesa.

In por baixo de, baixo is part of a fixed expression meaning under/below. It does not change to match mesa.

So you say:

• por baixo da mesa
• por baixo da cadeira
• por baixo do sofá

It stays baixo in this expression.

Yes. Debaixo da mesa is very common and often sounds more direct for physical position.

So these are both possible:

• O gato está por baixo da mesa
• O gato está debaixo da mesa

For many everyday situations, debaixo de is the more common straightforward way to say under. But por baixo de is also correct and natural.

Yes, it is natural and correct.

That said, many speakers would also very naturally say:

• O gato está debaixo da mesa.

So the sentence you have is good Portuguese, but a learner should also recognise debaixo de, because it is extremely common in Portugal.

Yes, but O gato está por baixo da mesa is the most neutral and standard order.

You may also hear or read:

• Por baixo da mesa está o gato.

This sounds more marked or literary, and it puts more focus on the location.

For normal conversation, the basic order is best:

• subject + verb + place
• O gato está por baixo da mesa.

The accent mark tells you that the stress falls on the last syllable:

• es-TÁ

That accent is important. Without it, esta is a different word:

• está = is
• esta = this

So the written accent helps both pronunciation and meaning.

Yes, but it changes the meaning.

• O gato está por baixo da mesa. = The cat is under the table.
• Um gato está por baixo da mesa. = A cat is under the table.

Use o when the cat is specific or already known. Use um when it is not specific or is being mentioned for the first time.

In this sentence, yes: da mesa is the normal form.

Portuguese often uses articles in places where English may or may not use them. Here, the table is expressed as:

• a mesa
• after contraction: da mesa

So por baixo mesa would be incorrect. You need the article:

• por baixo da mesa

Not very well.

A word-for-word breakdown is roughly:

• O = the
• gato = cat
• está = is
• por baixo de = under / underneath
• a mesa = the table

But languages do not always match word for word. The best approach is to understand the structure as:

• O gato = the cat
• está = is
• por baixo da mesa = under the table

So it is better to learn chunks like por baixo de than to force an exact one-word English match.