Мне ужасно нравится эта книга.

Because нравиться works differently from English to like.

In Russian, the thing being liked is the grammatical subject, and the person who experiences the feeling goes in the dative case.

So:

• мне = to me
• эта книга = this book
• нравится = is pleasing / appeals

A very literal translation is:

• Мне ужасно нравится эта книга.
• To me, this book is extremely pleasing.

That is why Russian uses мне, not я.

Because the subject is эта книга, which is singular.

Even though English says I like this book, Russian grammar is built around this book pleases me, so the verb agrees with книга, not with me.

Compare:

• Мне нравится эта книга. = I like this book.
• Мне нравятся эти книги. = I like these books.

In the second sentence, книги is plural, so the verb becomes нравятся.

Here ужасно means terribly, awfully, or more naturally in English, really / very / extremely.

It originally comes from the idea of horror / something ужасное, but in everyday speech it is often just an intensifier.

So in this sentence:

• ужасно нравится = like very much / really like

It does not mean that the speaker feels horror about the book. It is just strong emphasis.

Because эта книга is the subject of нравится, so it stays in the nominative case.

This is one of the biggest differences from English. In English, the thing you like is the object:

• I like this book

But with нравиться, that thing is the subject:

• Эта книга нравится мне

So nominative is correct:

• эта книга = nominative singular feminine

If you used эту книгу, that would be accusative, and that would not fit this structure.

Yes. Russian word order is flexible, and the basic meaning stays the same.

All of these can mean essentially the same thing:

• Мне ужасно нравится эта книга.
• Эта книга мне ужасно нравится.
• Эта книга ужасно мне нравится.
• Ужасно мне нравится эта книга.

But the emphasis changes.

For example:

• Мне ужасно нравится эта книга. → neutral, common
• Эта книга мне ужасно нравится. → focuses more on this book
• Ужасно мне нравится эта книга. → stronger emotional emphasis

For learners, the original order is a very natural one to use.

Yes, you can, but it is not exactly the same in tone.

• Мне ужасно нравится эта книга = I like this book very much
• Я ужасно люблю эту книгу = I love this book very much

Любить is usually stronger than нравиться.

Also notice the structure changes:

• with нравиться: мне
  • эта книга
• with любить: я
  • эту книгу

That is because любить works more like English to love, taking a direct object in the accusative:

• Я люблю эту книгу.

So yes, it is possible, but it expresses a stronger feeling.

Нравится is the 3rd person singular present tense form of нравиться.

Why 3rd person singular?

Because the subject is эта книга = this book, which is:

• third person
• singular

So:

• эта книга нравится
• эти книги нравятся

Also, the ending -ся is part of the verb. You should learn it as нравиться, not as plain нравить for normal everyday use.

This is the difference between imperfective and perfective aspect.

• нравится = likes / is pleasing / generally appeals
• понравится = will like / will come to like / will find pleasing

Examples:

• Мне нравится эта книга. = I like this book.
• Думаю, мне понравится эта книга. = I think I will like this book.

In your sentence, нравится is used because it describes a current feeling, not a future or completed reaction.

Because ужасно here is an adverb.

Adverbs often modify verbs or whole statements, and many of them end in -о:

• ужасно
• очень
• сильно
• быстро

In Мне ужасно нравится эта книга, it modifies нравится:

• ужасно нравится = likes very much

It is not describing книга. If you wanted to describe the book itself as terrible, you would need an adjective agreeing with книга:

• Это ужасная книга. = This is a terrible book.

So:

• ужасно нравится = like very much
• ужасная книга = a terrible book

Yes, очень is more neutral and more universally usable.

Compare:

• Мне очень нравится эта книга. = I like this book very much.
• Мне ужасно нравится эта книга. = I really / absolutely / terribly like this book.

Ужасно sounds more emotional and expressive. It is common, but less neutral than очень.

So if you are unsure, очень is the safer everyday choice. If you want stronger feeling, ужасно works well.

The main stress pattern is:

• мне
• ужа́сно
• нра́вится
• э́та
• кни́га

So the sentence is pronounced roughly like:

• Мне ужа́сно нра́вится э́та кни́га.

Stress matters in Russian, so it is worth learning each word with its stress from the beginning.