Primeiro eu limpo a pia com a esponja e depois passo o aspirador na sala.

Yes—Brazilian Portuguese often leaves out subject pronouns when the verb ending already makes the subject clear.

• limpo already means I clean
• passo already means I pass / I vacuum

So Primeiro limpo a pia... would also be correct.

Here, eu is included because:

• it can sound clearer at the start of a sentence
• it can add a little emphasis
• speakers sometimes include it and sometimes omit it naturally

Notice that the second eu is omitted in depois passo o aspirador, because the subject is still obviously I.

Limpo is the conjugated form of limpar for I in the present tense.

• limpar = to clean
• eu limpo = I clean

So this sentence uses a normal conjugated verb, not the infinitive.

This present tense can be used for:

• a routine: First I clean the sink...
• a sequence of actions being described in real time
• instructions or a step-by-step description

Yes. limpo can be:

• a verb: I clean
• an adjective: clean

Here it is clearly a verb because it follows eu and takes an object:

• eu limpo a pia = I clean the sink

If it were an adjective, the structure would be different, like:

• O chão está limpo = The floor is clean

Portuguese uses definite articles more often than English does.

In this sentence:

• a pia = the sink
• a esponja = the sponge
• o aspirador = the vacuum cleaner
• na sala = in the living room / room

Even when English might say with a sponge or just vacuum the living room, Portuguese often prefers the definite article when the object is understood from the situation.

So this sounds very natural in Portuguese.

Both are possible, but they mean slightly different things.

• com a esponja = with the sponge
  
  • the speaker has a specific sponge in mind
  • often the normal/expected sponge in that context
• com uma esponja = with a sponge
  
  • any sponge
  • less specific

In everyday Portuguese, com a esponja sounds very natural if the sponge is just the obvious tool being used.

Pia usually means sink.

Depending on context, it can refer to:

• a kitchen sink
• a bathroom sink / washbasin

In this sentence, because of esponja, many learners would picture a kitchen sink, but the word itself does not have to be only kitchen-related.

Because passar o aspirador is a very common expression in Brazilian Portuguese.

Literally, it is something like:

• to pass the vacuum cleaner

But naturally, it means:

• to vacuum

This is one of those actions that Portuguese often expresses with passar + tool/object.

You may also hear:

• aspirar a sala = to vacuum the room

But passar o aspirador is very common and very natural in everyday speech.

Yes, in Brazilian Portuguese you may hear both:

• passo o aspirador
• passo aspirador

The version with the article, passo o aspirador, is very common and often taught first.

The version without the article can sound a bit more colloquial or compact in some contexts. Both are understandable and natural in Brazil.

Because na is a contraction:

• em + a = na

So:

• na sala = in the room / in the living room

This kind of contraction is extremely common in Portuguese.

Other examples:

• no = em + o
• da = de + a
• do = de + o

You should think of na sala as the normal form, not as a shortened optional form.

It can mean either, depending on context.

Sala often means:

• living room
• sitting room
• sometimes just room or hall in certain contexts

In a household cleaning sentence like this, na sala will very often be understood as in the living room.

If you wanted to be more specific, you might say:

• sala de estar = living room

It is not required, but it is very natural because it clearly shows sequence.

• primeiro = first
• depois = then / afterwards

Together, they make the order of actions very clear:

1. clean the sink
2. vacuum the living room

You could also say:

• Primeiro eu limpo a pia. Depois passo o aspirador na sala.
• Eu limpo a pia e depois passo o aspirador na sala.

But Primeiro ... e depois ... is a very natural way to organize the sentence.

Because Portuguese often omits a repeated subject when it is still the same person.

So after Primeiro eu limpo..., it is natural to continue with:

• e depois passo...

The subject is still clearly I.

You could say:

• e depois eu passo o aspirador na sala

But leaving out the second eu is usually smoother and more natural.

The given word order is very natural, but Portuguese allows some flexibility.

For example, these are also possible:

• Eu primeiro limpo a pia e depois passo o aspirador na sala.
• Primeiro, limpo a pia com a esponja e depois passo o aspirador na sala.
• Depois, passo o aspirador na sala, mas primeiro limpo a pia com a esponja.

Still, the original version sounds very normal and clear:

• Primeiro eu limpo a pia com a esponja e depois passo o aspirador na sala.

It is a good model for expressing a sequence of everyday actions.