Eu quero aproveitar melhor meu tempo livre hoje.

Yes. In Portuguese, subject pronouns are often omitted because the verb ending already tells you who the subject is.

• quero = I want
• so Eu quero... and Quero... both work

Using eu can add:

• emphasis
• contrast
• clarity

So:

• Eu quero aproveitar melhor meu tempo livre hoje = natural
• Quero aproveitar melhor meu tempo livre hoje = also very natural

After querer, Portuguese normally uses the infinitive directly.

• quero aproveitar = I want to make good use of / enjoy
• literally, it is I want make use of...

Portuguese does not need a separate word like English to in this structure.

More examples:

• Quero estudar = I want to study
• Quero sair = I want to go out
• Quero descansar = I want to rest

So querer + infinitive is the normal pattern.

Aproveitar is a very useful verb with a broad meaning. Depending on context, it can mean:

• to enjoy
• to make good use of
• to take advantage of
• to make the most of

In this sentence, the idea is closest to:

• make better use of my free time
• or make the most of my free time

So it is not just passive enjoyment. It suggests using that free time in a worthwhile way.

Examples:

• Quero aproveitar o dia = I want to make the most of the day
• Aproveita a oportunidade = Take advantage of the opportunity
• Aproveitei muito a viagem = I really enjoyed the trip

Because melhor means better, while bem means well.

Compare:

• aproveitar bem = to make good use of, to use well
• aproveitar melhor = to make better use of, to use better

Since the sentence has the idea of improvement, melhor is the right choice.

So:

• Quero aproveitar bem meu tempo livre hoje = I want to use my free time well today
• Quero aproveitar melhor meu tempo livre hoje = I want to use my free time better today

Here melhor is modifying the verb aproveitar, so it works like an adverb: to use better.

That is why aproveitar melhor sounds natural.

The most common order is:

• verb + melhor + object

So:

• aproveitar melhor meu tempo livre

This is the most straightforward and natural phrasing.

You could sometimes move things around for emphasis, but this version is the normal one.

Both are possible.

In Brazilian Portuguese, possessives can appear:

• without an article: meu tempo livre
• with an article: o meu tempo livre

In many everyday sentences, especially after a verb, dropping the article sounds very natural.

So these are both acceptable:

• Quero aproveitar melhor meu tempo livre hoje
• Quero aproveitar melhor o meu tempo livre hoje

The version without the article is a little lighter and very common.

Yes. Possessive words agree with the thing possessed.

• tempo is masculine singular
• so the possessive is meu

Compare:

• meu tempo = my time
• minha rotina = my routine
• meus planos = my plans
• minhas horas livres = my free hours

So meu is used because tempo is masculine singular.

No, livre tempo is not natural here.

In Portuguese, many adjectives come after the noun, and tempo livre is a fixed, very common expression meaning free time.

So:

• tempo livre = correct
• livre tempo = not natural

This is similar to other common noun + adjective combinations in Portuguese:

• café quente = hot coffee
• casa grande = big house
• tempo livre = free time

In this sentence, hoje most naturally modifies the whole idea: today, I want to make better use of my free time.

It tells you when this desire or plan applies.

So the meaning is not really:

• my free time that is today

It is more like:

• today, I want to use my free time better

That is why hoje at the end sounds very natural.

Yes. Portuguese allows some flexibility with adverbs like hoje.

All of these are natural:

• Eu quero aproveitar melhor meu tempo livre hoje
• Hoje eu quero aproveitar melhor meu tempo livre
• Eu quero hoje aproveitar melhor meu tempo livre — possible, but less neutral

The most common choices are usually:

• at the beginning, for emphasis on today
• at the end, in a neutral sentence

So your original sentence sounds very good.

Yes, it is natural and correct.

A Brazilian might also say:

• Quero aproveitar melhor meu tempo livre hoje
• Hoje quero aproveitar melhor meu tempo livre
• Quero curtir mais meu tempo livre hoje

But the meaning changes slightly with different verbs:

• aproveitar = make good use of / make the most of
• curtir = enjoy, have fun with
• usar melhor = use better

Your sentence is a good, natural way to express a thoughtful intention.

Quero is the first person singular present indicative of querer.

So:

• eu quero = I want

Other forms:

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

In this sentence, the present tense expresses a current desire or intention for today.

A broad pronunciation guide is:

• Eu = eh-oo / ew
• quero = KEH-ro
• aproveitar = a-pro-vey-TAR
• melhor = meh-LYOR or sometimes closer to mi-LYOR
• meu = meh-oo blended into one syllable, roughly mew
• tempo livre = TEM-po LEE-vree
• hoje = OH-zhee

A more IPA-style version is roughly:

• Eu quero aproveitar melhor meu tempo livre hoje
• /ew ˈkɛ.ɾu a.pɾo.vejˈtaʁ meˈʎɔʁ mew ˈtẽ.pu ˈliv.ɾi ˈo.ʒi/

A few sounds English speakers often notice:

• lh in melhor is a palatal sound, similar to the lli in some pronunciations of million
• j in hoje sounds like the s in measure
• the r in quero is usually a light flap in Brazilian Portuguese