Prefiero aquel libro.

Because the verb is preferir, and in the present tense it has a stem change: e → ie in most forms.

So:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos/ellas prefieren

This is a very common pattern in Spanish. So prefiero is the correct I prefer form.

Spanish often omits subject pronouns because the verb ending already shows who is doing the action.
In prefiero, the ending -o tells you the subject is I.

So both are possible:

• Prefiero aquel libro.
• Yo prefiero aquel libro.

The version without yo is the most neutral and natural. Adding yo usually gives extra emphasis, contrast, or clarity.

Aquel is a demonstrative adjective meaning that ... over there or that one over there when it comes before a noun.

Spanish traditionally has a three-way contrast:

• este libro = this book (near me)
• ese libro = that book (near you / not very far)
• aquel libro = that book over there (far from both of us)

In real modern speech, especially casually, ese is often used more broadly for that, but aquel is still perfectly correct and is useful when you want to stress greater distance.

Both can often translate as that, but they do not suggest the same distance.

• ese libro usually points to something not near the speaker, but not necessarily very far away
• aquel libro suggests something farther away or more clearly distant

So aquel is the more distal choice. In English, we usually just say that book, so this extra distinction can feel new to learners.

Because aquel has to agree with the noun in gender and number.

Libro is masculine singular, so the correct form is aquel.

The forms are:

• aquel libro = masculine singular
• aquella casa = feminine singular
• aquellos libros = masculine plural
• aquellas casas = feminine plural

So the form changes to match the noun it describes.

Because demonstratives like este, ese, aquel normally go before the noun when they are used as adjectives.

So:

• aquel libro
• esa mesa
• estos zapatos

If the noun is omitted, then the demonstrative can stand alone as a pronoun:

• Prefiero aquel. = I prefer that one.

In your sentence, aquel is describing libro, so it comes before it.

No. The personal a is generally used before a specific person (and sometimes a pet or personified animal) when that person is the direct object.

Compare:

• Veo a María.
• Prefiero aquel libro.

Since libro is a thing, not a person, there is no personal a here.

Aquel is pronounced roughly ah-KEL.

The spelling qu before e or i represents a k sound in Spanish, and the u is silent:

• que = keh
• quien = kyen
• aquel = ah-kel

So in aquel, you do not pronounce the u.

Because aquel does not take a written accent here.

In this sentence, aquel is clearly a demonstrative adjective because it comes before a noun: libro.
Also, in modern Spanish spelling, demonstratives such as este, ese, aquel are normally written without accent marks, even when they are pronouns.

So aquel libro is the standard spelling.

Yes. That is completely correct.

• Prefiero aquel libro. = neutral, natural
• Yo prefiero aquel libro. = more emphatic

You might use yo if you are contrasting with someone else:

• Tú prefieres este, pero yo prefiero aquel libro.

So the version without yo is more basic, but both are fine.

Yes, but the normal, neutral order is exactly what you have: Prefiero aquel libro.

Spanish word order is somewhat flexible, but changing it usually adds emphasis or sounds more marked:

• Prefiero aquel libro. = neutral
• Aquel libro prefiero. = unusual on its own; sounds emphatic or literary
• Yo prefiero aquel libro. = emphasis on I

So for everyday use, your sentence is the best standard pattern.