Learn Hardcore Portuguese (Brazil): Eu quero conhecer o autor do livro.

conhecer:
- to meet someone for the first time: Quero conhecer o autor. = I want to meet the author.
- to be acquainted with / to know (people, places, things): Eu conheço o autor. = I know the author (personally / I’m familiar with him).
saber:
- to know facts, information, or how to do something:
  - Eu sei quem é o autor. = I know who the author is.
  - Eu sei escrever. = I know how to write.

If you said Eu quero saber o autor do livro, it would sound odd; you’d normally say Eu quero saber quem é o autor do livro (I want to know who the author is), not saber o autor.

Why is it quero and not querer or quer?

Quero is the conjugated form of the verb querer (to want) for eu (I) in the present tense:

infinitive: querer = to want
present tense, eu form: eu quero = I want

Quer (without o) is the ele/ela/você form:

Ele quer conhecer o autor. = He wants to meet the author.

So:

Eu quero conhecer… = correct
Eu querer conhecer… = wrong (using infinitive where conjugation is needed)
Eu quer conhecer… = wrong (using the wrong person/ending)

Can I omit Eu and just say Quero conhecer o autor do livro?

Yes. In Brazilian Portuguese, it is very common (and natural) to drop the subject pronoun when the verb ending makes the subject clear.

Eu quero conhecer o autor do livro.
Quero conhecer o autor do livro.

Both mean I want to meet the author of the book.
In speech, Quero conhecer… is actually more typical and sounds very natural.

Why is it conhecer o autor and not conhecer ao autor, like Spanish conocer al autor?

Portuguese does not use a personal “a” before human direct objects the way Spanish does.

Spanish: Quiero conocer al autor. (a + el)
Portuguese: Quero conhecer o autor. (no preposition)

In conhecer o autor, o autor is a direct object, and you simply use the definite article o, without a in front of it.
Conhecer ao autor is incorrect in Brazilian Portuguese in this meaning.

Why do we need o in o autor do livro? Could I just say Eu quero conhecer autor do livro?

In Portuguese, a singular, countable noun that is specific almost always needs a definite article (o, a, os, as).

o autor = the author (a specific author)
autor alone sounds incomplete/unnatural in this context.

Eu quero conhecer autor do livro sounds wrong.
You need:

Eu quero conhecer o autor do livro. = I want to meet the author of the book (a particular one).

What is do in do livro? Why not de o livro?

Do is a contraction of de + o:

de = of / from
o = the (masculine singular)
de + o = do

So:

o autor do livro = the author of the book

Portuguese always contracts certain prepositions with definite articles:

de + o = do (of the)
de + a = da (of the, feminine)
de + os = dos (of the, plural masculine)
de + as = das (of the, plural feminine)

You normally must use the contraction, not de o in standard language.

Can I change the word order, like Eu quero o autor do livro conhecer?

No, that word order is very unnatural in modern Brazilian Portuguese.

The normal, neutral order here is:

Eu quero conhecer o autor do livro.
[subject] [conjugated verb] [infinitive] [object]

You can drop Eu, but you still keep the same verb order:

Quero conhecer o autor do livro.

Structures like quero o autor do livro conhecer are not used in everyday Brazilian Portuguese.

How would I say I would like to meet the author of the book (more polite)?

A common, more polite version is:

Eu gostaria de conhecer o autor do livro.

Pattern:

gostaria de + infinitive = would like to + verb
- Eu gostaria de falar. = I would like to speak.
- Eu gostaria de conhecer. = I would like to meet.

You can also drop Eu:

Gostaria de conhecer o autor do livro.

Does conhecer here mean to meet for the first time or to know someone already?

In Eu quero conhecer o autor do livro, it usually implies:

to meet (for the first time) / to get to know the author.

Context can extend it to:

to get to know better: maybe you’ve heard of the author but don’t know him personally.

But the basic idea with conhecer + a person (in this kind of sentence) is personal contact, not just intellectual knowledge.

How do I say I want to know who the author of the book is, not I want to meet the author?

If you mean know the information, you use saber, not conhecer:

Eu quero saber quem é o autor do livro.
= I want to know who the author of the book is.

So:

Quero conhecer o autor do livro. → I want to meet / get to know him.
Quero saber quem é o autor do livro. → I want to know (find out) who he is.

How would the sentence change for a female author or for multiple authors?

Female author (a autora):
- Eu quero conhecer a autora do livro.
  (a = feminine singular article, autora = feminine of autor)
Multiple authors (os autores):
- Eu quero conhecer os autores do livro. = I want to meet the authors of the book.
- If the book has multiple books (the books of the author):
  - Eu quero conhecer o autor dos livros. = I want to meet the author of the books.
    (dos = de + os, of the [plural])

Is this sentence formal, informal, or neutral in Brazilian Portuguese?

Eu quero conhecer o autor do livro. is neutral and fine in most situations.

Informal, natural:
- Quero conhecer o autor do livro. (dropping Eu)
More polite / softer:
- Eu gostaria de conhecer o autor do livro.
- Gostaria de conhecer o autor do livro.

You would choose gostaria de instead of quero in more formal or especially polite contexts.