Quero cantar um dueto e um solo.

In Brazilian Portuguese, the subject pronoun is often omitted when it is already clear from the verb form.

• Quero already means I want
• So Quero cantar... naturally means I want to sing...

You can also say:

• Eu quero cantar um dueto e um solo.

That is also correct, but eu is not necessary here. Adding eu can give a little extra emphasis or contrast, depending on the context.

Quero is the first-person singular form of the verb querer (to want).

Present tense of querer:

• eu quero = I want
• você quer = you want
• ele/ela quer = he/she wants
• nós queremos = we want
• vocês querem = you all want
• eles/elas querem = they want

So in this sentence, quero tells you the speaker is talking about themself: I want.

After querer, Portuguese usually uses another verb in the infinitive.

So the pattern is:

• querer + infinitive

Examples:

• Quero cantar. = I want to sing.
• Quero comer. = I want to eat.
• Quero sair. = I want to leave.

That is why the sentence uses quero cantar, not a conjugated form like quero canto.

Portuguese often repeats the article when talking about two separate nouns.

So:

• um dueto e um solo sounds complete and natural

It clearly means:

• one duet
• and one solo

Sometimes in Portuguese an article can be omitted in coordinated phrases, but here repeating um is the most standard and natural choice.

Because dueto and solo are masculine nouns in Portuguese, they normally take the masculine singular indefinite article um.

• um dueto
• um solo

If a noun were feminine, you would use uma instead:

• uma canção
• uma apresentação

There is not always a perfect logical reason for noun gender, so often you simply learn the noun together with its article.

Yes, dueto is a correct and understood word in Brazilian Portuguese. It means a duet, especially in music.

You may also hear related expressions such as:

• cantar em dueto = to sing as a duet / in duet form
• fazer um dueto = to do a duet

So cantar um dueto is understandable and correct. Depending on context, some speakers might also phrase the idea differently, but this sentence is perfectly fine.

They are related, but not exactly the same.

• cantar um solo = to sing a solo piece / perform a solo
• cantar solo = to sing alone / sing solo

In your sentence, um solo is a noun, meaning a solo performance or solo number.

So:

• Quero cantar um dueto e um solo. = I want to sing a duet and a solo.

A simple approximation is:

• KEH-ro can-TAR oong doo-EH-too ee oong SOH-loo

A few pronunciation notes:

• quero: stress on que
• cantar: stress on the last syllable -tar
• dueto: usually pronounced with three syllables, du-e-to
• solo: stress on so
• um often sounds nasal in Portuguese, not like English oom

This is only an approximation for English speakers, but it can help you get started.

The original order is the most natural:

• Quero cantar um dueto e um solo.

You can add the subject:

• Eu quero cantar um dueto e um solo.

But you generally would not move things around in an English-like way such as:

• Quero um dueto e um solo cantar. ❌

Portuguese word order is fairly flexible in some cases, but with querer + infinitive + object, the sentence as given is the normal structure.

Yes. With e, the sentence means the speaker wants to sing both:

• a duet
• and a solo

If the speaker meant one or the other, Portuguese would use ou:

• Quero cantar um dueto ou um solo. = I want to sing a duet or a solo.

So e clearly signals addition, not choice.