Depois da faxina, eu consegui montar a cama perto do ventilador.

Because depois normally uses the preposition de, and faxina here has the definite article a:

• depois de + a faxina → depois da faxina

So da is just the contraction of de + a.

This structure is very common in Portuguese:

• depois da aula
• depois do almoço
• depois da reunião

Faxina usually means cleaning, especially a more thorough cleaning of a room, house, or apartment.

So depois da faxina suggests:

• after the cleaning
• after doing the house cleaning
• after tidying/cleaning up

In Brazil, fazer faxina is a very common expression for doing house cleaning.

Yes, eu could be omitted.

Portuguese often drops subject pronouns when the verb ending already makes the subject clear. Since consegui clearly means I managed / I was able, you can say:

• Depois da faxina, consegui montar a cama perto do ventilador.

Adding eu makes the subject more explicit. It can sound:

• a little more emphatic
• a little clearer in context
• slightly more natural in some spoken situations

So both are correct.

Consegui is the pretérito perfeito of conseguir.

Here it means:

• I managed
• I succeeded in
• I was able to

It refers to a completed action in the past. The idea is that the speaker successfully did it.

Compare:

• Eu consigo = I can / I manage
• Eu conseguia = I used to be able to / I was managing
• Eu consegui = I managed / I was able to

After conseguir, Portuguese normally uses an infinitive to say what someone managed to do:

• consegui montar = managed to assemble
• consegui terminar = managed to finish
• consegui encontrar = managed to find

So the pattern is:

• conseguir + infinitive

That is why montar stays in the infinitive form.

Usually, no. In this sentence, montar a cama most naturally means assemble the bed or put the bed together.

That is because montar often means:

• assemble
• set up
• put together

If you want to say make the bed in the everyday sense of arranging the sheets and blankets, Brazilian Portuguese usually says:

• arrumar a cama

So:

• montar a cama = assemble the bed
• arrumar a cama = make/tidy the bed

Portuguese uses definite articles more often than English does.

So where English might say:

• assemble a bed near a fan

Portuguese may naturally say:

• montar a cama perto do ventilador

The articles a and o do not always mean a very specific object in the same strong way as the in English. Often they are just part of normal, natural Portuguese phrasing.

Here:

• a cama = the bed
• o ventilador = the fan

Because perto normally comes with the preposition de:

• perto de

Since ventilador is masculine and uses the article o, you get:

• perto de + o ventilador → perto do ventilador

So do is the contraction of de + o.

Examples:

• perto da janela
• perto do sofá
• perto de mim

Yes. Perto do ventilador and próximo do ventilador both mean near the fan.

In everyday Brazilian Portuguese:

• perto de is extremely common and very natural
• próximo de is also correct, but can sound a bit more formal depending on context

So this would also work:

• Depois da faxina, eu consegui montar a cama próximo do ventilador.

The sentence order is natural, but Portuguese has some flexibility.

The original order is very standard:

• Depois da faxina = time expression first
• eu consegui = subject + verb
• montar a cama = what was done
• perto do ventilador = location

You could also say:

• Eu consegui montar a cama perto do ventilador depois da faxina.

That still works, but it places the time expression at the end instead of the beginning.

The original version sounds smooth and natural because it sets the scene first: After cleaning, I managed...

Yes, it can suggest either one, depending on context.

Most naturally, it means the bed was assembled in a position near the fan, or that the final placement of the bed is near the fan. Portuguese often leaves this kind of detail to context.

If you wanted to be more explicit, you could say:

• eu consegui montar a cama e colocá-la perto do ventilador = I managed to assemble the bed and put it near the fan
• eu consegui montar a cama que estava perto do ventilador = I managed to assemble the bed that was near the fan

But in the original sentence, the meaning is simply that the bed is associated with that location.

A simple pronunciation guide would be:

deh-POYJ dah fah-SHEE-nah, eh-oo kohn-seh-GEE mon-TAR ah KAH-mah PEHR-too doo ven-chee-lah-DOR

A few helpful notes:

• depois often sounds like depóis
• faxina has a shi sound in many Brazilian accents: fa-SHEE-na
• consegui is stressed on the last syllable: con-se-GUI
• ventilador is stressed on the last syllable: ven-ti-la-DOR

Pronunciation varies by region, but this is a good Brazil-oriented starting point.

Yes, and the meaning stays very close.

Compare:

• Depois da faxina = After the cleaning / After cleaning up
• Depois de limpar = After cleaning

The first uses a noun (faxina). The second uses a verb (limpar).

Both are natural, but depois da faxina can sound a bit more like after the whole cleaning task was done, especially house cleaning.