Quiero aprovechar las vacaciones para estudiar español con calma.

In Spanish, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• quiero = I want
• The -o ending tells you it is yo

So Quiero aprovechar... is completely natural. You can say Yo quiero aprovechar..., but adding yo usually gives extra emphasis, contrast, or clarity.

For example:

• Quiero estudiar español. = neutral
• Yo quiero estudiar español. = I want to study Spanish (maybe unlike someone else)

Aprovechar often means to make good use of, to take advantage of, or to make the most of something.

In this sentence, aprovechar las vacaciones means using the holiday time in a useful or productive way.

It is a very common verb in Spanish, especially in sentences like:

• Quiero aprovechar el tiempo. = I want to make good use of the time.
• Aprovecha la oportunidad. = Take advantage of the opportunity.
• Voy a aprovechar el fin de semana para descansar. = I’m going to make the most of the weekend to rest.

So here it suggests not just having holidays, but using them well for a purpose.

In Spanish, vacaciones is normally used in the plural, even when English might use vacation in the singular.

So:

• las vacaciones = holiday time / vacation / the holidays

This is standard Spanish, including Spain. You would usually not say la vacación for this meaning in everyday speech.

Examples:

• Estoy de vacaciones. = I’m on holiday / on vacation.
• Las vacaciones de verano = the summer holidays

Spanish often uses the definite article more than English does. Here, las vacaciones refers to a specific period of holidays that the speaker has in mind.

So Quiero aprovechar las vacaciones... sounds natural because it means something like:

• I want to make the most of the holidays / my holiday period

Even if English might say during vacation or on my holiday, Spanish commonly says las vacaciones.

Para + infinitive is a very common structure used to express purpose: in order to, so as to, for the purpose of.

So:

• para estudiar español = in order to study Spanish

The sentence structure is:

• Quiero aprovechar las vacaciones = I want to make good use of the holidays
• para estudiar español = in order to study Spanish

Other examples:

• Voy al supermercado para comprar pan. = I’m going to the supermarket to buy bread.
• Necesito tiempo para pensar. = I need time to think.

Because after querer (to want), Spanish normally uses another verb in the infinitive.

So the pattern is:

• querer + infinitive

Examples:

• Quiero dormir. = I want to sleep.
• Queremos viajar. = We want to travel.
• Quiero aprovechar las vacaciones para estudiar español.

This is similar to English want to + verb, except Spanish does not use a separate word for to here before the second verb.

After verbs like estudiar, hablar, aprender, and enseñar, the names of languages are often used without an article.

So:

• estudiar español = to study Spanish
• hablo inglés = I speak English
• aprende francés = he/she learns French

You may see el español in other contexts, especially when talking about the language more generally as a subject or concept:

• El español es una lengua muy hablada. = Spanish is a widely spoken language.

But after estudiar, no article is the normal choice.

Con calma is a very common expression meaning:

• calmly
• without rushing
• at a relaxed pace
• taking your time

So estudiar español con calma means studying Spanish in a relaxed, unhurried way.

It does not only mean being emotionally calm. It often suggests doing something carefully and without pressure.

Examples:

• Vamos con calma. = Let’s take it easy / let’s go slowly.
• Léelo con calma. = Read it carefully / take your time reading it.
• Quiero hablar contigo con calma. = I want to talk to you properly / calmly / without rushing.

Yes, in many cases you could say tranquilamente, but it is not always exactly the same in tone.

• con calma sounds very natural and everyday
• tranquilamente is also correct, but it can sound a bit more formal or more like peacefully/calmly

Compare:

• estudiar español con calma = to study Spanish at a relaxed pace
• estudiar español tranquilamente = to study Spanish calmly / peacefully

In this sentence, con calma is probably the most natural choice.

Spanish word order is fairly flexible, but this order is the most neutral and natural.

The basic structure is:

• Quiero = main verb
• aprovechar las vacaciones = what I want to do
• para estudiar español = purpose
• con calma = manner, how I want to study

So the sentence builds in a very clear way:

1. I want...
2. to make good use of the holidays...
3. in order to study Spanish...
4. in a relaxed way

You could move parts around for emphasis, but the original version sounds smooth and natural.

Yes, but it would change the meaning slightly.

• Quiero aprovechar las vacaciones para estudiar español con calma.
  = I want to make the most of the holidays in order to study Spanish calmly.

• Quiero estudiar español con calma durante las vacaciones.
  = I want to study Spanish calmly during the holidays.

The second version focuses more on when you will study.
The original focuses more on using the holidays well for that purpose.

Both are correct, but they are not quite identical in nuance.

In Spain, vacaciones usually refers to a break from work or school: what British English often calls holidays and American English often calls vacation.

So depending on the variety of English, las vacaciones may be translated as:

• the holidays
• vacation
• the vacation period

In Spanish from Spain, it is a very common everyday word:

• las vacaciones de verano = summer holidays
• las vacaciones de Navidad = Christmas holidays

A helpful approximate pronunciation is:

• Quiero → KYE-ro
• aprovechar → a-pro-be-CHAR
• las vacaciones → las ba-ka-THYO-nes in most of Spain
  or las ba-ka-SYO-nes in Latin American pronunciation
• para estudiar → PA-ra es-tu-DYAR
• español → es-pa-NYOL
• con calma → kon KAL-ma

A few pronunciation notes for Spain:

• v and b sound very similar
• ci in vacaciones is usually pronounced like th in much of Spain
• ñ in español sounds like the ny in canyon
• the stress in español falls on the last syllable: -ñol

Yes, it sounds completely natural in Spanish from Spain.

It is a very normal kind of sentence because it uses several common patterns:

• querer + infinitive
• aprovechar + time period/opportunity
• para + infinitive for purpose
• con calma for doing something without rushing

A native speaker in Spain could easily say this exactly as it appears.