Este libro es suyo.

Este is the demonstrative adjective for this. It usually refers to something close to the speaker, or something the speaker feels is mentally close in the context.

• este libro = this book
• ese libro = that book (near the listener, or not near the speaker)
• aquel libro = that book over there (far from both)

So Este libro es suyo specifically means this book is his/hers/yours/theirs.

Because Spanish uses ser for identification, classification, and possession in sentences like this.

Here, the sentence is saying who the book belongs to, not where it is or what temporary state it is in.

• Este libro es suyo. = The book belongs to him/her/etc.
• Este libro está en la mesa. = The book is on the table.

A useful shortcut:

• ser = identity / essential relationship
• estar = location / temporary condition

Suyo is a stressed possessive form meaning:

• his
• hers
• its
• yours (formal)
• theirs

In English, after to be, we often use forms like mine, yours, his, hers, theirs. Spanish does something similar:

• Es mío = It’s mine.
• Es tuyo = It’s yours.
• Es suyo = It’s his/hers/yours/theirs.

So in this sentence, suyo means belonging to that person / those people.

Because su and suyo are used in different structures.

• su goes before a noun:

  • su libro = his/her/your/their book

• suyo is used when the possessive stands more independently, often after ser:

  • El libro es suyo = The book is his/hers/yours/theirs

So:

• Este es su libro. = This is his/her/your/their book.
• Este libro es suyo. = This book is his/hers/yours/theirs.

Both are correct, but the grammar pattern is different.

Because suyo agrees with the thing owned, not with the owner.

Here, the thing owned is libro, which is:

• masculine
• singular

So the possessive form must also be masculine singular:

• libro → suyo

Compare:

• La casa es suya. = The house is his/hers/etc.
• Los libros son suyos. = The books are his/hers/etc.
• Las llaves son suyas. = The keys are his/hers/etc.

This is a very common point of confusion for English speakers, because English does not change his/hers/their to match the noun in this way.

Yes, suyo is ambiguous on its own. It can mean:

• his
• hers
• its
• your (formal singular: usted)
• their
• sometimes your formal plural (ustedes)

In Spain specifically, informal plural your is usually vuestro/a/os/as, not suyo, but suyo is still used for formal usted/ustedes and for third person.

If Spanish needs to be clearer, it often adds:

• de él = his
• de ella = hers
• de usted = yours (formal singular)
• de ellos = theirs
• de ellas = theirs

For example:

• Este libro es suyo, de ella.
• Este libro es de él.

Because es suyo is the normal way to say it is his/hers/etc.

After ser, Spanish often uses the possessive directly:

• Es mío.
• Es tuyo.
• Es suyo.

You can use el suyo in some contexts, but it usually sounds more contrastive or specific, like his/hers one or the one that belongs to him/her.

Compare:

• Este libro es suyo. = This book is his/hers.
• Este libro es el suyo, no el mío. = This book is his/hers one, not mine.

So in your sentence, no article is the most natural basic form.

Yes. That is also correct.

The two sentences are very close in meaning:

• Este es su libro.
• Este libro es suyo.

The difference is mostly one of structure and focus:

• Este es su libro = This is his/her/their book

  • You identify this thing as his/her/their book.

• Este libro es suyo = This book is his/hers/theirs

  • You start with this book and then say who it belongs to.

In many situations, either one works.

In modern standard Spanish, no.

The recommended spelling is:

• este libro

Older rules sometimes allowed or preferred an accent in some pronoun uses, like éste, but current standard usage normally does not use it.

In your sentence, este is clearly an adjective before libro, so este without an accent is definitely correct.

The normal, neutral order is:

• Este libro es suyo.

That is what learners should use.

Other orders are possible, but they are marked or literary:

• Suyo es este libro.

That sounds much less neutral and would usually be used only for emphasis or a stylistic effect.

So for everyday Spanish, stick with Este libro es suyo.