Eu quero conhecer o autor do livro.

In Eu quero conhecer o autor do livro, conhecer means to meet / to get to know (personally).

• 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.

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)

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.

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.

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).

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.

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.

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.

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.

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.

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.