No hay libros en ninguna parte.

Because hay means there is / there are in the sense of existence.

• Hay libros = There are books
• Están los libros would mean the books are somewhere, referring to specific books whose location you already know or are discussing.

So in No hay libros en ninguna parte, the idea is not where certain books are, but that no books exist anywhere.

In Spanish, standard negation usually puts no before the verb.

• No hay libros = There are no books

You do not normally say Hay no libros in Spanish.

This is one of the most basic word-order rules for negation:

• No tengo dinero
• No viene nadie
• No hay libros

Hay is an impersonal form of the verb haber.

It is used to say that something exists or is present:

• Hay un libro = There is a book
• Hay libros = There are books

Important points:

• Hay does not change for singular or plural.
  
  • Hay un libro
  • Hay dos libros
• It is not the same as he, has, ha, etc., which are other forms of haber used in perfect tenses.

Yes, it is a double negative, and that is completely normal in Spanish.

Spanish often uses negative concord, which means multiple negative words can appear together in the same sentence:

• No veo nada = I don’t see anything
• No vino nadie = Nobody came
• No hay libros en ninguna parte = There are no books anywhere

In English, we usually avoid double negatives in standard grammar, but in Spanish they are often required.

Ninguna parte means no part / no place, and in the expression en ninguna parte it means nowhere or anywhere in a negative sentence.

So:

• en ninguna parte = nowhere / anywhere

Examples:

• No lo encuentro en ninguna parte = I can’t find it anywhere
• No hay libros en ninguna parte = There are no books anywhere

Because parte is a feminine noun:

• la parte

So the adjective must agree with it:

• ninguna parte

Compare:

• ningún libro = no book / not any book
• ninguna casa = no house / not any house

Before a singular masculine noun, ninguno becomes ningún:

• ningún libro
• ningún problema

But with a feminine noun, it stays ninguna:

• ninguna parte
• ninguna idea

Yes. Por ninguna parte is also very common and often sounds especially natural in everyday Spanish.

Both are correct:

• No hay libros en ninguna parte
• No hay libros por ninguna parte

They both mean roughly There are no books anywhere.

A slight nuance:

• en ninguna parte = more neutral, standard
• por ninguna parte = often feels a bit more idiomatic in speech, like nowhere at all

Yes, that is grammatically correct, but the meaning shifts slightly.

• No hay libros en ninguna parte = There are no books anywhere
  This is a general statement about books in the plural.
• No hay ningún libro en ninguna parte = There isn’t a single book anywhere
  This can sound a bit more emphatic.

So the version with ningún libro highlights the absence of even one book.

In Spanish, after hay, plural countable nouns often appear without an article when speaking generally.

• Hay libros = There are books
• Hay coches fuera = There are cars outside

Adding an article changes the meaning:

• Hay libros = books exist / there are some books
• Están los libros = the books are there
• Hay unos libros = there are some books (less neutral, more specific)

So in this sentence, bare plural libros is the natural general form.

Yes, but only when it comes before the verb.

Spanish negative words can appear without no if they are placed before the verb:

• Nadie vino = Nobody came
• Nada pasó = Nothing happened
• En ninguna parte hay libros = Nowhere are there books

But if the negative word comes after the verb, you need no:

• No hay libros en ninguna parte

So both of these are correct:

• En ninguna parte hay libros
• No hay libros en ninguna parte

It is grammatical, but it is less neutral than No hay libros en ninguna parte.

Starting with En ninguna parte gives the sentence a more marked or emphatic feel, as if you are stressing nowhere.

• Neutral: No hay libros en ninguna parte
• More emphatic/literary: En ninguna parte hay libros

In everyday conversation, the original sentence is usually the more natural choice.

A careful Spain Spanish pronunciation would be approximately:

No ay lee-bros en neen-GOO-na PAR-te

A few useful notes:

• h in hay is silent.
• hay sounds a bit like English eye, but with an a starting sound: ay.
• ll in libros in most of Spain sounds like y.
• z does not appear here, so there is no special Spain-only sound in this sentence.
• Stress:
  • libros → LI-bros
  • ninguna → nin-GU-na
  • parte → PAR-te

It is neutral standard Spanish.

You can use it in:

• conversation
• writing
• descriptions
• narration

It does not sound especially formal or especially casual. It is just a normal, correct way to say that there are no books anywhere.