La bibliothèque a une salle d’informatique et un laboratoire de physique.

In French, la bibliothèque means library (a place where you borrow/read books, often free).

La librairie is a bookstore (a shop where you buy books).
So:

• la bibliothèque = library
• la librairie = bookstore

This is a classic false friend for English speakers.

The verb avoir (here: a) is used to express possession: the library has these rooms.

• La bibliothèque a une salle d’informatique… = The library has a computer room…

You could also say:

• Il y a une salle d’informatique dans la bibliothèque.
  = There is a computer room in the library.

But La bibliothèque est une salle d’informatique would mean the library is a computer room, which is wrong here: the library is not identical to the room; it just possesses it.

All three can refer to rooms, but they’re used differently:

• une salle – a room for a specific function, often public or institutional:

  • salle de classe (classroom)
  • salle de réunion (meeting room)
  • salle d’informatique (IT / computer room)

• une pièce – a general room in a house/apartment:

  • une pièce de la maison (a room in the house)
  • un appartement de trois pièces (a three-room apartment)

• une chambre – a bedroom (place where you sleep).

In this sentence, salle is correct because it’s a specialized room in a public place (the library).

Literally:

• salle d’informatique = room of computing / IT room / computer room

Grammatically, it’s salle de informatique, but de becomes d’ before a vowel sound:

• de + informatique → d’informatique

This is called elision, and it’s mandatory in writing and speech:
you cannot say salle de informatique.

French often uses the field or activity word after de / d’ to name specialized rooms:

• salle d’informatique – IT / computer room
• salle de musique – music room
• salle de sport – gym / sports hall

You could say salle avec des ordinateurs (room with computers), but that just describes the content, not the official type of room. The natural, institutional term is salle d’informatique.

No. Another false friend:

• l’informatique = computing, computer science, IT in general
• information in French is information (usually uncountable) or des informations (pieces of information)

So salle d’informatique is about computers/IT, not about information in the everyday sense.

In French, de + field is the standard way to say a lab of a certain specialty:

• un laboratoire de physique – a physics lab
• un laboratoire de chimie – a chemistry lab
• un laboratoire de biologie – a biology lab

Using de here indicates the type of laboratory.

En is more often used for:

• someone’s specialization: être spécialisé en physique
• a field of study: un cours en physique

So for naming the lab itself, de is the normal choice: laboratoire de physique.

When de + noun indicates the type or field, French usually omits the article:

• un cours de français (a French course)
• un professeur de physique (a physics teacher)
• un laboratoire de physique (a physics lab)

Adding an article would change the meaning:

• le laboratoire de la physique would sound like “the laboratory of Physics (as a personified entity)” or of some specific physics we’ve already identified. That’s not what we want here; we just want the kind of lab, so it’s de physique with no article.

Because:

• salle is a feminine noun → une salle
• laboratoire is a masculine noun → un laboratoire

You can see this in the articles and in any adjectives that would follow:

• une grande salle moderne (feminine adjectives)
• un grand laboratoire moderne (masculine adjectives)

French noun gender is mostly arbitrary and has to be memorized with the noun.

In French, common nouns almost always need an article (definite, indefinite, or partitive).
Here, la is the definite article:

• La bibliothèque = The library

Using Bibliothèque with no article is only normal when:

• it’s part of an institution’s proper name, e.g. Bibliothèque nationale de France, or
• in titles/headings, where articles are often dropped.

In a normal sentence, you say La bibliothèque.

Yes, that version is perfectly correct:

• La bibliothèque a un laboratoire de physique et une salle d’informatique.

French allows either order when simply listing two items. The meaning doesn’t change; you just change the emphasis slightly (the item mentioned first can feel a bit more prominent).

You would make the nouns and articles plural:

• La bibliothèque a des salles d’informatique et des laboratoires de physique.

Details:

• une salle → des salles
• un laboratoire → des laboratoires
• The d’ in d’informatique stays the same because it’s still de + informatique, and elision still applies.