Me gusta escuchar la radio por la mañana mientras desayuno.

Because gustar works differently from to like in English.

In Spanish, gustar literally works more like to be pleasing to. So:

• Me gusta escuchar la radio = Listening to the radio is pleasing to me
• not I like in the same grammatical structure as English

So:

• me = to me
• gusta = is pleasing

That is why yo gusto is usually not the right way to say I like.
Yo gusto would mean something more like I am pleasing / I am liked, depending on context.

Me is an indirect object pronoun, and here it means to me.

In the sentence:

• Me gusta escuchar la radio

the full idea is:

• A mí me gusta escuchar la radio = I like listening to the radio

Spanish often includes this little pronoun with gustar:

• me = to me
• te = to you
• le = to him/her/you
• nos = to us
• os = to you all
• les = to them/you all

So me gusta is the normal way to say I like.

Because the thing being liked is treated as singular.

Here, what follows gusta is:

• escuchar la radio = listening to the radio

That whole infinitive phrase acts like one singular idea, so Spanish uses gusta.

Compare:

• Me gusta escuchar la radio. = I like listening to the radio.
• Me gustan las canciones. = I like the songs.

Use:

• gusta with a singular noun or an infinitive
• gustan with a plural noun

After gustar, Spanish normally uses the infinitive when talking about liking an action.

So:

• Me gusta escuchar la radio = I like listening to the radio

Not:

• Me gusta escucho ❌
• Me gusta escuchando ❌

This is similar to other Spanish patterns:

• Quiero comer = I want to eat
• Prefiero leer = I prefer to read
• Me encanta viajar = I love travelling

So escuchar is correct because it names the activity itself.

In Spanish, it is very common to use the definite article with things like radio, television, body parts, and many general nouns where English might leave it out.

So Spanish says:

• escuchar la radio = listen to the radio
• ver la televisión = watch television / watch TV

Even if English sometimes drops the article, Spanish often keeps it.

In this sentence, la radio is the normal and natural choice.

Both can relate to hearing, but they are not exactly the same.

• oír = to hear
• escuchar = to listen

So:

• Oigo la radio = I hear the radio
• Escucho la radio = I listen to the radio

In your sentence, escuchar is used because it suggests deliberate attention, not just passive hearing.

This is a fixed and very common expression in Spanish.

• por la mañana = in the morning
• por la tarde = in the afternoon / evening
• por la noche = at night / in the evening

You should mostly learn it as a set phrase rather than translating por word for word.

So even though por often means for, by, or through, in this expression por la mañana simply means in the morning.

After mientras, Spanish normally uses a conjugated verb, not a gerund.

So:

• mientras desayuno = while I have breakfast / while I’m having breakfast

Not:

• mientras desayunando ❌

This is a very common structure:

• mientras estudio = while I study / while I’m studying
• mientras trabajo = while I work / while I’m working

So desayuno is correct because it is the present tense form of desayunar.

Here, desayuno is the present indicative, and in this kind of sentence it can correspond to either:

• while I have breakfast
• while I’m having breakfast

Spanish often uses the simple present where English may choose either the simple present or the present continuous, depending on context.

So:

• mientras desayuno can mean while I eat breakfast or while I’m eating breakfast

Both ideas fit naturally.

Because Spanish often leaves out subject pronouns when the verb ending already shows who the subject is.

• desayuno already means I have breakfast / I eat breakfast

So yo is not necessary.

You could say:

• mientras yo desayuno

but that usually adds emphasis or contrast. In a normal sentence, Spanish prefers:

• mientras desayuno

You could, but it is less natural here.

In Spanish, desayunar is the usual verb for to have breakfast. So:

• mientras desayuno = while I have breakfast

is more idiomatic than:

• mientras como el desayuno = while I eat breakfast

Also, el desayuno sounds more specific, like the breakfast as a meal. In everyday speech, desayunar is simpler and more natural.

Yes, Spanish word order is fairly flexible, though some versions sound more natural than others.

For example, these are possible:

• Me gusta escuchar la radio por la mañana mientras desayuno.
• Por la mañana me gusta escuchar la radio mientras desayuno.
• Mientras desayuno, me gusta escuchar la radio por la mañana.

The original sentence sounds very natural. If you move things around, the emphasis changes a little:

• Por la mañana at the front emphasizes the time
• Mientras desayuno at the front emphasizes the simultaneous action

But the basic meaning stays the same.

Yes, it sounds perfectly natural in Spain.

A few points that fit standard Spain Spanish well:

• escuchar la radio is completely normal
• por la mañana is the standard expression
• desayuno for I have breakfast is very natural

So a learner of Spanish from Spain can treat this as a good, everyday model sentence.