Eu tenho vergonha de falar com o professor.

Yes. You can often omit eu in Portuguese because the verb form tenho already shows that the subject is I.

So both of these are natural:

• Eu tenho vergonha de falar com o professor.
• Tenho vergonha de falar com o professor.

Including eu can add emphasis, contrast, or clarity.

For example:

• Eu tenho vergonha, mas minha amiga não.
• Tenho vergonha de falar com o professor. = a neutral statement

Portuguese often uses the expression ter vergonha literally, to have shame/embarrassment/shyness, where English might prefer to be embarrassed, to feel shy, or to be ashamed.

This is just a normal Portuguese structure:

• ter vergonha de... = to be embarrassed/ashamed/shy about...
• estar com vergonha = to be feeling embarrassed/shy

So tenho vergonha is not strange at all; it is one of the standard ways to express this idea.

Vergonha can cover a few related ideas in Portuguese, depending on context:

• embarrassment
• shame
• shyness / self-consciousness

In this sentence, it often sounds like:

• feeling shy about speaking to the teacher
• feeling embarrassed to speak to the teacher
• feeling uncomfortable doing it

So vergonha is broader than any single English word. Context tells you which shade is strongest.

Because vergonha commonly takes de before the thing that causes the feeling or before an action.

Common patterns:

• vergonha de + noun
  • Tenho vergonha do meu erro.
• vergonha de + infinitive
  • Tenho vergonha de falar em público.

So in your sentence:

• de falar = about speaking / to speak

This is just the normal preposition used with vergonha.

Because after de, Portuguese uses the infinitive when talking about an action in a general way.

So:

• de falar = to speak / speaking
• not de falo

This is similar to English patterns like:

• afraid to speak
• embarrassed to speak
• tired of speaking

In Portuguese, after many nouns, adjectives, and verbs, the infinitive is very common.

Yes, other options exist, but falar com is the most natural choice here if the idea is to speak with / talk to someone.

Here is the difference in feel:

• falar com o professor = to talk with/to the teacher; very common and neutral
• falar ao professor = more formal, less common in everyday Brazilian Portuguese
• falar para o professor = also common in Brazil, often sounds like speaking to him, directing speech toward him

In everyday Brazilian Portuguese, falar com is usually the safest and most natural option for a conversation.

Portuguese uses definite articles much more often than English does, especially before specific people identified by role or profession.

So if you mean a particular teacher, o professor sounds natural:

• Vou falar com o professor.
• A professora chegou.

In English, you often say the teacher too, but Portuguese may use the article even in places where English would not.

If you were addressing the teacher directly, that would be different:

• Professor, posso entrar?
• Professora, tenho uma dúvida.

There, the article is usually dropped because it is direct address.

Usually, yes. In Portuguese, professor is masculine and normally refers to a male teacher.

If the teacher is female, you would usually say:

• a professora

So the sentence would become:

• Eu tenho vergonha de falar com a professora.

Portuguese marks gender much more visibly in nouns and articles than English does.

Yes, absolutely. In Brazilian Portuguese, both are common, but they can feel slightly different.

• Tenho vergonha de falar com o professor.
  • a general personal tendency, or simply a neutral statement
• Estou com vergonha de falar com o professor.
  • emphasizes the current feeling right now

In real conversation, Brazilians often use estar com vergonha when talking about a present situation.

Examples:

• Estou com vergonha de perguntar.
• Ela está com vergonha de cantar.

So your original sentence is correct, but estou com vergonha is also very natural.

Usually, the normal order is:

• Eu tenho vergonha de falar com o professor.

You can also omit eu:

• Tenho vergonha de falar com o professor.

Putting eu later is possible only in special structures, usually for emphasis, and is less neutral. For a learner, it is best to keep:

• Eu tenho... or
• Tenho...

That is the most natural pattern.

It is neutral and natural. It works well in everyday speech and writing.

Nothing in it is especially slangy or especially formal:

• eu tenho = standard
• vergonha de = standard
• falar com = very common in spoken Brazilian Portuguese
• o professor = standard

So this is a good sentence to learn as a normal, everyday structure.

A helpful approximate pronunciation is:

• ver-GON-ya

A few notes:

• lh in Portuguese is a special sound, often like ly in million, though the exact sound is different.
• The stress is on gon: ver-GON-ha
• In Brazilian Portuguese, the final a is often light.

A rough full-sentence pronunciation guide:

• Eu tenho vergonha de falar com o professor.
• eh-ooh TEN-yo ver-GON-ya dji fah-LAR kohm oo pro-feh-SOR

That is only an approximation, but it can help at the beginning.

Yes, but the meaning shifts a little.

• falar com o professor = to speak/talk to the teacher
• conversar com o professor = to have a conversation with the teacher

Conversar sounds a bit more like an actual back-and-forth conversation, while falar is broader and more flexible.

So:

• Tenho vergonha de falar com o professor. = very natural
• Tenho vergonha de conversar com o professor. = also natural, but slightly more specific

It is:

• Eu = subject
• tenho = verb
• vergonha = noun
• de falar = prepositional phrase with infinitive
• com o professor = who the speaking is directed to

So the pattern is:

• [subject] + ter + vergonha de + infinitive + com/alguém

You can use this pattern with many other verbs:

• Tenho vergonha de perguntar.
• Tenho vergonha de cantar.
• Tenho vergonha de falar em público.

This makes the sentence a very useful model to copy.