Mi hermana quiere ser periodista y escribir un reportaje sobre el cambio climático.

In modern standard Spanish, you normally use the short possessive adjective before the noun:

• mi hermana = my sister
• tu hermano = your brother
• su casa = his/her/their house

Using la mi hermana is not standard modern Spanish. Spanish does have longer possessive forms like mío, tuyo, suyo, but those are usually used after the noun or on their own:

• una hermana mía = a sister of mine
• Esta hermana es mía = This sister is mine

So mi hermana is simply the normal way to say my sister.

After querer (to want), Spanish usually uses an infinitive if the subject is the same person doing both actions.

Here, mi hermana is the subject of everything:

• mi hermana quiere = my sister wants
• ser periodista = to be a journalist
• escribir un reportaje = to write a report/article

So the structure is:

• [subject] + querer + infinitive

Examples:

• Quiero comer. = I want to eat.
• Queremos viajar. = We want to travel.
• Mi hermana quiere ser periodista. = My sister wants to be a journalist.

You do not need que here because there is no change of subject.

Because que is usually used when the second verb has a different subject.

Compare:

• Mi hermana quiere ser periodista.
  My sister wants to be a journalist.
  → Same subject: my sister wants, and my sister will be the journalist.

• Mi hermana quiere que yo sea periodista.
  My sister wants me to be a journalist.
  → Different subjects: my sister wants, but I would be the journalist.

So in your sentence, quiere + infinitive is correct because the same person is doing both actions.

Because ser is used for identity, profession, and more permanent characteristics.

A job or profession is treated as part of what someone is, not a temporary state:

• ser periodista = to be a journalist
• ser médico = to be a doctor
• ser estudiante = to be a student

Estar is used for states, conditions, or locations:

• estar cansado = to be tired
• estar en Madrid = to be in Madrid

So periodista is a profession, which is why ser is the right verb.

After ser, professions usually appear without an article when you are simply naming the profession.

• Mi hermana quiere ser periodista.
• Su padre es profesor.
• Ella es ingeniera.

You can use an article if you are adding description or emphasis:

• Mi hermana quiere ser una periodista famosa.
• Es un periodista excelente.

So in your sentence, ser periodista is the normal, neutral way to express the profession.

Usually, periodista has the same form for both men and women. The article or context shows the gender:

• el periodista = the male journalist
• la periodista = the female journalist

In your sentence, mi hermana makes it clear the person is female, so periodista refers to a woman even though the noun itself stays the same.

This is common with many nouns ending in -ista:

• el/la artista
• el/la dentista
• el/la turista

Because Spanish, like English, can coordinate two infinitives after one verb of wanting.

So:

• quiere ser periodista y escribir un reportaje

means:

• she wants to be a journalist and write a report/article

The verb quiere applies to both infinitives:

• ser
• escribir

You could repeat it, but it would sound heavier and usually unnecessary:

• Mi hermana quiere ser periodista y quiere escribir un reportaje.

That is grammatical, but less natural here unless you want extra emphasis.

Reportaje often means a report, feature report, or article/reportage, depending on context.

In journalism, it usually suggests something more developed than a very short news item. It can be:

• a magazine feature
• a newspaper report
• a TV/radio report
• an in-depth journalistic piece

So escribir un reportaje suggests writing a journalistic piece about the topic, not just any random school report.

The preposition sobre often means about or on when introducing a topic.

So:

• un reportaje sobre el cambio climático = a report/article about climate change

Other examples:

• un libro sobre historia = a book about history
• hablar sobre política = to talk about politics

Here, sobre introduces what the report is about.

In Spanish, many abstract or general concepts often appear with the definite article where English may not use one.

So Spanish commonly says:

• el cambio climático
• la educación
• la salud
• el amor

Even though English often says just climate change, Spanish naturally says el cambio climático in many contexts.

Could you sometimes see cambio climático without the article? Yes, especially in headlines, labels, or very compressed styles. But in a normal sentence like this, sobre el cambio climático is the most natural choice.

Because the written accent shows the stress falls on -má-:

• cli-má-ti-co

Without the accent, normal stress rules would suggest a different pronunciation. The accent mark makes the correct stress clear.

This matters because Spanish spelling often tells you exactly where the stress goes.

The most direct reading is that she wants both:

• to be a journalist
• to write a report on climate change

The sentence does not explicitly say one action is the purpose of the other. It simply links two desired actions with y (and).

If you wanted to make the idea of purpose clearer, Spanish would often use something like:

• Mi hermana quiere ser periodista para escribir un reportaje sobre el cambio climático.

That would mean more specifically:

• My sister wants to be a journalist in order to write a report on climate change.

So your original sentence is best understood as a simple list of two things she wants to do.

The sentence follows a very natural Spanish order:

• Mi hermana — subject
• quiere — main verb
• ser periodista y escribir un reportaje sobre el cambio climático — what she wants to do

This is straightforward and neutral. Spanish can sometimes vary word order for emphasis, but this version is the most standard.

For example, you could move things around in special contexts, but this would usually sound less neutral:

• Quiere mi hermana ser periodista...
• Escribir un reportaje sobre el cambio climático quiere mi hermana...

Those are possible only in marked or literary contexts. For normal speech and writing, the original order is the best choice.