Mi hermano pequeño tiene diecinueve años, pero todavía le da vergüenza hablar en público.

Because in Spanish, age is expressed with tener (to have), not ser or estar.

So:

• Tiene diecinueve años = He is nineteen years old
• Literally: He has nineteen years

This is one of the most important differences from English:

• I am 20 → Tengo veinte años
• She is 15 → Tiene quince años

Using es diecinueve años would be incorrect.

In Spanish, adjectives often come after the noun, so hermano pequeño is the normal order.

• mi hermano pequeño = my little/younger brother

If you put the adjective before the noun, it can sound more literary, emotional, or stylistically marked:

• mi pequeño hermano might sound more affectionate or descriptive, but it is less neutral here.

Also, in real usage, hermano pequeño often means younger brother, not necessarily a physically small brother.

It can mean either, depending on context, but very often it means younger brother.

In this sentence, since we are told he is nineteen years old, pequeño clearly does not mean he is a small child. It most naturally means:

• my younger brother

Spanish often uses pequeño this way in family relationships:

• mi hermana pequeña = my younger sister

This is a very common Spanish structure:

• dar vergüenza a alguien = to make someone feel embarrassed / to embarrass someone

So:

• le = to him
• da = gives
• vergüenza = embarrassment / shame

Literally, le da vergüenza hablar en público is something like:

• Speaking in public gives him embarrassment

More natural English:

• He is embarrassed to speak in public
• Speaking in public embarrasses him
• He feels shy about speaking in public

Spanish often expresses feelings this way, with the thing causing the feeling as the grammatical subject.

Le is an indirect object pronoun, and here it means to him.

In le da vergüenza hablar en público:

• le = to him
• da vergüenza = causes embarrassment

So the sentence is saying that speaking in public causes embarrassment to him.

This is the same kind of pattern as:

• Le gusta el chocolate = He/She likes chocolate
• Le duele la cabeza = His/Her head hurts
• Le da miedo conducir = Driving scares him/her

The person feeling something is often marked with an indirect object pronoun in Spanish.

Grammatically, the subject is the whole idea hablar en público.

So:

• Hablar en público = speaking in public
• le da vergüenza = causes him embarrassment

In other words:

• Hablar en público le da vergüenza
• Speaking in public embarrasses him

Spanish often places the infinitive phrase after the verb, but it is still the thing producing the feeling.

Because Spanish uses the infinitive very often where English uses an -ing form.

So:

• hablar en público = speaking in public / to speak in public

After expressions like dar vergüenza, gustar, molestar, encantar, and many others, Spanish commonly uses the infinitive:

• Me gusta leer = I like reading / I like to read
• Le molesta esperar = Waiting annoys him
• Nos da miedo volar = Flying scares us

Using hablando here would be wrong.

These are related, but they are not used in the same way.

• vergüenza = shame / embarrassment / shyness, depending on context
• tener vergüenza can mean to be modest, to feel shame, or sometimes to have a sense of decency
• dar vergüenza means to cause embarrassment

Examples:

• Me da vergüenza hablar en público = I’m embarrassed to speak in public
• Tiene vergüenza = He is shy / He feels embarrassed / He has shame
• Eso da vergüenza = That is embarrassing / That’s shameful

In your sentence, dar vergüenza is the important structure.

Todavía means still here, and it adds the idea that this is surprising or continuing up to now.

• pero le da vergüenza hablar en público = but he is embarrassed to speak in public
• pero todavía le da vergüenza hablar en público = but he is still embarrassed to speak in public

So todavía emphasizes that even at nineteen, this continues.

You could also sometimes use aún in similar contexts:

• pero aún le da vergüenza...

In everyday Spanish, todavía is extremely common.

Because pero introduces a contrast between two clauses, and Spanish normally separates those clauses with a comma.

Here the contrast is:

• He is nineteen years old
• but he is still embarrassed to speak in public

So the comma is standard:

• ..., pero ...

This is very similar to English punctuation in many cases.

En público means in public or in front of other people.

It is a fixed and very common expression:

• hablar en público = to speak in public
• cantar en público = to sing in public
• aparecer en público = to appear in public

It does not mean speaking to the audience in the sense of direction. It means doing something publicly, where other people are present.

Yes. Avergonzar is a verb meaning to embarrass.

So:

• Le da vergüenza hablar en público
• Le avergüenza hablar en público

Both are possible, but dar vergüenza is often more common and more natural in everyday speech.

A small nuance:

• le da vergüenza often feels very idiomatic and common for personal embarrassment or shyness
• le avergüenza can sound a little more direct or slightly more formal, depending on context

Because Spanish often leaves out subject pronouns when they are clear from the context.

Here:

• Mi hermano pequeño already tells us who we are talking about
• tiene and da are both third-person singular forms

So adding él would usually be unnecessary:

• Mi hermano pequeño tiene diecinueve años, pero todavía le da vergüenza hablar en público.

Spanish prefers to omit subject pronouns unless they are needed for emphasis, contrast, or clarity.

Yes, vergüenza covers a range of meanings including:

• embarrassment
• shame
• shyness

In this sentence, the most natural sense is something like:

• embarrassment
• self-consciousness
• shyness

So he feels shy/embarrassed about speaking in public is probably the best interpretation. Shame in a stronger moral sense would be less likely here.