Minha prima trabalha na empresa onde eu quero trabalhar no próximo ano.

Because prima is a feminine noun in Portuguese, so it takes the feminine possessive minha.

• minha prima = my female cousin
• meu primo = my male cousin

The possessive has to agree with the noun being possessed, not with the speaker.

Prima means female cousin.

Portuguese usually distinguishes male and female cousins:

• primo = male cousin
• prima = female cousin

So Minha prima specifically means my female cousin.

Na is a contraction of em + a.

• em = in, at
• a = the for a feminine singular noun
• empresa is feminine, so a empresa = the company

So:

• na empresa = in/at the company

This kind of contraction is very common in Portuguese:

• no = em + o
• na = em + a
• nos = em + os
• nas = em + as

Onde means where, and it refers to a place.

In this sentence, a empresa is a place or location, so onde works naturally:

• a empresa onde eu quero trabalhar = the company where I want to work

In Brazilian Portuguese, this is very common and natural.

You may also hear:

• a empresa em que eu quero trabalhar

That is also correct and slightly more formal.

Not by itself. After trabalhar, Portuguese normally needs the preposition em when you mean work at/in a place.

So the correct versions are:

• a empresa onde eu quero trabalhar
• a empresa em que eu quero trabalhar
• a empresa na qual eu quero trabalhar (more formal)

But a empresa que eu quero trabalhar sounds incomplete, because the idea of in/at is missing.

Because they are different verb forms.

• trabalha = works
  This is the present tense, third person singular, for ela/você.

  • Minha prima trabalha = My cousin works

• trabalhar = to work
  This is the infinitive.

  • eu quero trabalhar = I want to work

After querer (to want), Portuguese normally uses an infinitive:

• quero estudar = I want to study
• quero viajar = I want to travel
• quero trabalhar = I want to work

Yes, Portuguese often can leave subject pronouns out, because the verb ending usually shows who the subject is.

So both of these are natural:

• onde eu quero trabalhar
• onde quero trabalhar

In Brazilian Portuguese, speakers often include pronouns like eu more than in European Portuguese, especially for clarity or emphasis. So using eu here sounds completely normal.

Yes, it is normal.

The sentence says:

• Minha prima trabalha... = My cousin works...
• eu quero trabalhar... = I want to work...

Even though English also repeats work, learners sometimes expect Portuguese to avoid repetition. But in this sentence, repeating trabalhar is natural and clear.

You could rephrase the sentence in other ways, but the original is perfectly normal.

No próximo ano means next year or more literally in the next year.

Again, no is a contraction:

• em + o = no

And ano is masculine:

• o ano = the year

So:

• no próximo ano = in the next year / next year

Also:

• próximo agrees with ano, so it is masculine singular
• if the noun were feminine, it would change:
  • na próxima semana = next week

Yes. In Brazilian Portuguese, ano que vem is very common in everyday speech.

So these are both natural:

• no próximo ano
• ano que vem

The difference is mostly style:

• no próximo ano sounds a bit more neutral or slightly more formal
• ano que vem sounds very common and conversational

For example:

• Minha prima trabalha na empresa onde eu quero trabalhar ano que vem.

That sounds very natural in Brazil.

A common rule is:

• onde = where, for location
• aonde = where to, for movement toward a place

Here, the idea is working at a company, not going to a company, so onde is the normal choice:

• a empresa onde eu quero trabalhar

You would use aonde more naturally with verbs like ir, levar, chegar in some contexts of movement:

• Aonde você quer ir? = Where do you want to go?

That said, in real speech, many native speakers do not always keep this distinction perfectly strict.

Yes, a little.

The original sentence is very natural:

• Minha prima trabalha na empresa onde eu quero trabalhar no próximo ano.

You could also say:

• Eu quero trabalhar no próximo ano na empresa onde minha prima trabalha.

This is also correct, but the focus changes a bit. The original starts with Minha prima, so it presents the cousin first. The alternative starts with Eu quero trabalhar, so it focuses more on your goal.

Portuguese word order is somewhat flexible, but not completely free. The original version is clear and idiomatic.

A more formal version could be:

• Minha prima trabalha na empresa em que eu quero trabalhar no próximo ano.
• Minha prima trabalha na empresa na qual eu quero trabalhar no próximo ano.

All of these are correct:

• onde = very natural
• em que = correct, a bit more formal
• na qual = more formal and more explicit

In everyday Brazilian Portuguese, onde is probably the most common choice here.

A rough pronunciation guide is:

• trabalha ≈ trah-BAHL-yah

A few helpful notes:

• lh in Portuguese sounds like the lli in million for many English speakers
• the stress is on ba: tra-BA-lha
• trabalhar sounds roughly like trah-bahl-YAR in many Brazilian accents

Also:

• minha ≈ MEEN-ya
• próximo ≈ PRO-see-mo or PROK-see-mo, depending on accent
• onde ≈ ON-jee or ON-djee in many Brazilian accents

These are only approximations, but they can help at the beginning.