Eu escuto o rádio.

Yes, you often can leave it out.

Portuguese verb endings usually show who is doing the action, so escuto already means I listen / I hear. Because of that, both of these are possible:

• Eu escuto o rádio.
• Escuto o rádio.

Including eu can add emphasis, contrast, or clarity. For example:

• Eu escuto o rádio, mas ele vê TV.
  = I listen to the radio, but he watches TV.

In everyday Brazilian Portuguese, subject pronouns are used more often than in some other varieties of Portuguese, but omission is still very common.

Escuto is the 1st person singular present tense of escutar.

The infinitive is:

• escutar = to listen

Present tense:

• eu escuto = I listen
• você escuta = you listen
• ele/ela escuta = he/she listens
• nós escutamos = we listen
• vocês escutam = you all listen
• eles/elas escutam = they listen

So in the sentence, escuto matches eu.

Both are possible, but they are not always used in exactly the same way.

• escutar often emphasizes listening
• ouvir often means to hear, but it can also mean to listen to

So these can both be natural:

• Eu escuto o rádio.
• Eu ouço o rádio.

In Brazilian Portuguese, ouvir is very common for music, radio, sounds, and speech.
Escutar is also common and perfectly correct.

A rough comparison:

• ouvir = hear / listen to
• escutar = listen to

But in real usage, there is a lot of overlap.

Because rádio is a masculine noun here, so the definite article is o:

• o rádio = the radio

In Portuguese, articles are used more often than in English. So a sentence with the in Portuguese may sound natural even when English would be more general.

That said, you may also hear:

• Eu escuto rádio.

This often sounds more general, like I listen to radio / I listen to the radio as an activity.

So the difference is roughly:

• Eu escuto o rádio. = I listen to the radio / the radio set / radio broadcasts
• Eu escuto rádio. = I listen to radio, in general

Both are possible.

Because grammatical gender in Portuguese is part of the noun itself, and rádio is normally masculine when it means radio.

So you say:

• o rádio
• um rádio
• meu rádio

Examples:

• O rádio está ligado. = The radio is on.
• Comprei um rádio novo. = I bought a new radio.

As with many nouns, the gender has to be learned together with the word.

The accent mark in rádio shows where the stress goes.

It is pronounced with stress on the ra part:

• RÁ-dio

Very roughly for an English speaker, it sounds like:

• HAH-jee-oo or RAH-dyoo, depending on accent

In Brazilian Portuguese, the final -dio is usually pronounced as something like jee-o in many regions, because di before o can sound softer. But exact pronunciation varies by region.

The most important point is:

• stress the first syllable: RÁdio

A simple approximate pronunciation is:

• eh-oos-coo-too oo RAH-dyoo

A more natural Brazilian-style approximation:

• eh-u es-KOO-tu u RAH-dju

A few notes:

• Eu is often pronounced something like eh-u or ehw
• escuto has stress on tu: es-CU-to
• o before a consonant is usually pronounced like oo
• rádio has stress on the first syllable: RÁ-dio

If you want a smoother rhythm, it sounds like:

• Eu escuto o rádio.
• eh-u es-KOO-tu u RAH-dju

Yes. That is completely natural.

Portuguese often allows the subject pronoun to be omitted when the verb already makes the subject clear:

• Escuto o rádio. = I listen to the radio.

This is especially common in context, for example if someone asks:

• O que você faz de manhã?
  What do you do in the morning?

You could answer:

• Escuto o rádio.

Yes, but Eu escuto o rádio is the most basic and neutral order.

Normal order is:

• subject + verb + object
• Eu + escuto + o rádio

You can also say:

• Escuto o rádio.
• O rádio, eu escuto todo dia.
  = The radio, I listen to every day.

That second kind of structure is more marked and usually used for emphasis or contrast.

So for a learner, the safest default is:

• Eu escuto o rádio.

It can mean either one, depending on context.

It may refer to:

• the radio set / device
• radio broadcasting / radio programs

Examples:

• O rádio está na cozinha.
  = The radio is in the kitchen.
  Here it clearly means the device.

• Eu escuto rádio todas as manhãs.
  = I listen to the radio every morning.
  Here it usually means radio programs or radio as a medium.

In Eu escuto o rádio, the meaning could be understood as listening to radio broadcasts, though context helps.

Yes, a Brazilian could say this. It is correct and natural.

But in everyday speech, some other very common versions are:

• Eu ouço rádio.
• Eu escuto rádio.
• Eu ouço o rádio.

All of these are normal. Which one sounds most natural can depend on region, context, and personal preference.

If you want a very common everyday phrasing for a general habit, many speakers would say:

• Eu ouço rádio.

But Eu escuto o rádio is absolutely fine.

The present tense in Portuguese can express either one, depending on context.

So Eu escuto o rádio can mean:

• I listen to the radio as a habit
• I am listening to the radio in some contexts

If you want to make right now extra clear in Brazilian Portuguese, people often use:

• Eu estou escutando o rádio.
• Eu estou ouvindo o rádio.

That means:

• I am listening to the radio

So the simple present is broader than English present simple in many situations.

No. Both with and without the article are possible.

Compare:

• Eu escuto o rádio.
• Eu escuto rádio.

Very roughly:

• with o: more specific, more like the radio
• without o: more general, more like radio as an activity or medium

This is not always a strict rule, but it is a useful guide for learners. Portuguese often allows both patterns depending on style and meaning.