Eu fiquei com vergonha de falar na frente de todos.

Yes. In Brazilian Portuguese, eu is often optional because the verb form fiquei already shows that the subject is I.

So both are natural:

• Eu fiquei com vergonha de falar na frente de todos.
• Fiquei com vergonha de falar na frente de todos.

Including eu can add a little emphasis, contrast, or clarity, but it is not required in normal conversation.

Fiquei is the pretérito perfeito form of ficar for eu.

In this sentence, ficar does not mean only to stay. It often means to become or to end up in a certain state.

So:

• ficar com vergonha = to become embarrassed / to get embarrassed / to feel embarrassed

That is why fiquei com vergonha sounds very natural in Portuguese. It describes a change into that emotional state.

Portuguese often expresses feelings with a noun phrase instead of a direct adjective.

Here:

• vergonha = shame / embarrassment
• com vergonha = literally with embarrassment, but naturally embarrassed

So ficar com vergonha is a very common structure in Portuguese.

You may also hear:

• estar com vergonha = to be embarrassed
• ter vergonha = to have embarrassment / to be ashamed or shy in a situation

English and Portuguese simply package the feeling differently.

They are similar, but not identical.

• fiquei com vergonha
  = I got embarrassed / I became embarrassed
  Focuses on the moment or change of state.

• estava com vergonha
  = I was embarrassed
  Describes an ongoing state in the past.

• tive vergonha
  = I felt ashamed / I was ashamed / I had embarrassment
  Possible, but in many everyday contexts fiquei com vergonha sounds more natural when describing becoming embarrassed in a specific moment.

So in your sentence, fiquei com vergonha is a very natural choice because it suggests that the situation caused the embarrassment.

After vergonha, Portuguese often uses de + infinitive to say embarrassed to do something or ashamed to do something.

So:

• vergonha de falar = embarrassed to speak
• vergonha de perguntar = embarrassed to ask
• vergonha de cantar = embarrassed to sing

This is a very common pattern:

• ter/ficar/estar com vergonha de + infinitive

Using para falar here would not sound natural for this meaning.

It means in front of everyone.

Breakdown:

• em = in
• a frente = the front
• em + a becomes na
• de todos = of everyone / of all

So:

• na frente de todos = in front of everyone

This is a fixed, very common expression.

Both exist, but they are used a little differently.

• na frente de todos = in front of everyone
• em frente a/de often refers more literally to physical position, especially with places or objects, like in front of the house

In many situations, na frente de todos is the most natural way to say in front of everyone in the sense of being publicly visible before a group.

So for speaking publicly before a group, na frente de todos fits very well.

Yes. Todos here means everyone or all the people there.

You could also say:

• na frente de todo mundo

That is very common in Brazilian Portuguese and often sounds even more conversational.

So these are both natural:

• na frente de todos
• na frente de todo mundo

The first can sound a little more neutral or structured; the second is very common in everyday speech.

No, this sentence stays the same.

• Eu fiquei com vergonha de falar na frente de todos.

Nothing in this sentence changes for the speaker’s gender.

That is because:

• fiquei does not change for gender
• vergonha is a noun, and its grammatical gender is always feminine, but that does not mean it refers only to women

If you used an adjective instead, then gender might matter, for example:

• Eu fiquei envergonhado. — male speaker
• Eu fiquei envergonhada. — female speaker

But with com vergonha, there is no change.

Yes, you could, and people would understand you. But eu fiquei com vergonha de falar na frente de todos usually sounds more natural if you mean I got embarrassed in that situation.

Very roughly:

• tive vergonha = I felt ashamed / I had embarrassment
• fiquei com vergonha = I became embarrassed / I got embarrassed

So the original sentence has a stronger sense that the embarrassment arose because of the situation.

Somewhat, yes, but the original order is very natural.

Original:

• Eu fiquei com vergonha de falar na frente de todos.

Possible variation:

• Eu fiquei com vergonha de falar na frente de todo mundo.
• Na frente de todos, eu fiquei com vergonha de falar.
  This is possible, but it sounds more marked or literary because it emphasizes the setting first.

For a learner, the original order is the safest and most natural.

Na is a contraction:

• em + a = na

So:

• na frente = em a frente, but Portuguese contracts it to na frente

This kind of contraction is very common in Portuguese:

• em + o = no
• de + o = do
• de + a = da

Learning these contractions is important because they appear constantly in everyday Portuguese.