Nesta semana, eu vou estudar português em casa.

Both are correct in Brazilian Portuguese.

• esta semana = this week
• nesta semana literally comes from em + esta semana, so it means in this week

In everyday Brazilian Portuguese, esta semana is often more common, but nesta semana is also natural and correct. In this sentence, nesta semana emphasizes the time frame a little more clearly: during this week.

Nesta is a contraction of:

• em = in
• esta = this

So:

• em esta → nesta

This kind of contraction is very common in Portuguese:

• em + este = neste
• em + essa = nessa
• em + aquele = naquele

So nesta semana literally means in this week.

In Brazilian Portuguese, using ir + infinitive is one of the most common ways to talk about the future.

• eu vou estudar = I am going to study / I will study

This is often more common in everyday speech than the simple future:

• estudarei

Both are correct, but they feel different:

• vou estudar = very common, natural, conversational
• estudarei = more formal, less common in casual speech

So this sentence sounds very natural in Brazilian Portuguese.

Yes. You can say:

• Nesta semana, vou estudar português em casa.

Portuguese often drops subject pronouns when the verb already makes the subject clear. Since vou clearly matches eu, the pronoun is optional.

However, keeping eu can help:

• add emphasis
• make the sentence clearer for learners
• create contrast, such as eu vou estudar, mas ele vai descansar

So both versions are correct.

In Portuguese, names of languages are normally not capitalized, unless they begin a sentence.

So:

• português
• inglês
• espanhol
• francês

This is different from English, where Portuguese, English, and Spanish are capitalized.

Em casa is the usual expression for at home or at home/in the house in a general sense.

• em casa = at home

You use na casa when you mean a specific house, often someone else's house or a particular house:

• Estou em casa. = I’m at home.
• Estou na casa da minha amiga. = I’m at my friend’s house.

So in your sentence, em casa is the natural choice because it means at home in a general way.

Because vou estudar works as a future expression:

• vou = I go / am going
• estudar = to study

Together, they mean am going to study / will study.

Then português is the thing being studied, so it comes after the verb:

• vou estudar português = I’m going to study Portuguese

This word order is normal in Portuguese and matches English fairly closely.

Usually, when talking about studying a language in general, Portuguese does not use the article here:

• estudar português = natural

Using o português can sound more specific, depending on context, such as:

• the Portuguese language as a subject in a particular setting
• a contrast with another language
• a more formal or stylistic choice

For a basic sentence like this, estudar português is the most natural option.

Yes, in most cases they mean basically the same thing: this week.

Possible nuance:

• Esta semana = this week
• Nesta semana = during this week / in this week

But in normal conversation, the difference is usually very small. A native speaker would understand either one easily.

In Brazilian Portuguese, português is approximately pronounced:

• por-too-GUES

A few helpful points:

• the stress is on the last syllable: -guês
• the ês sound is nasal-free here, just a stressed vowel sound
• the final s in Brazilian Portuguese is usually like an s sound in many regions, though pronunciation can vary by accent

Also notice the accent mark:

• português

The accent shows the stressed syllable.

The comma separates the time expression from the rest of the sentence.

• Nesta semana, eu vou estudar português em casa.

This is very common when a sentence begins with a time phrase like:

• Hoje,
• Amanhã,
• Na segunda-feira,
• Neste mês,

The comma helps readability. In informal writing, some people may leave it out, but using it is standard and correct.

Yes. In many contexts, eu vou estudar can be translated either way in English:

• I am going to study Portuguese at home this week
• I will study Portuguese at home this week

The Portuguese form itself does not force one exact English future meaning. The best translation depends on context and style.

Yes, that is also correct.

Portuguese allows some flexibility in word order, especially with time expressions. These are both natural:

• Nesta semana, eu vou estudar português em casa.
• Eu vou estudar português em casa nesta semana.

The first version puts the time first, which gives it a little more emphasis. The second sounds slightly more neutral in flow. Both are good.