Mis amigas y yo estamos en la biblioteca, y cada una lee un libro diferente.

Because mis is the plural form of the possessive.

• mi amiga = my friend
• mis amigas = my friends

The possessive has to match the number of the thing possessed, not the owner.

Amigas is feminine plural, so it tells you the friends are female.

• amigas = female friends
• amigos = male friends, or a mixed group

Since the sentence says Mis amigas y yo, the speaker is grouping herself with female friends.

Both are understandable, but Mis amigas y yo sounds more natural and polite in Spanish, just like my friends and I is usually preferred in English over I and my friends.

Putting yo later is very common in coordinated subjects.

Because estar is used for location.

• estamos en la biblioteca = we are in the library
• somos would describe identity or essential characteristics, not where someone is

So for places, Spanish normally uses estar:

• Estoy en casa
• Estamos en Madrid
• Ellas están en la biblioteca

Spanish often omits subject pronouns because the verb ending already shows who the subject is.

• estamos already means we are

So:

• Mis amigas y yo estamos en la biblioteca is natural
• Nosotras estamos en la biblioteca is also possible, but usually only if you want emphasis or contrast

Because en shows location: being in / at a place.

• estamos en la biblioteca = we are in the library

By contrast, a usually shows movement toward a place:

• Vamos a la biblioteca = we are going to the library

So:

• en = location
• a = destination

Cada una means each one, and here it refers to each of the female people in the group.

• cada = each
• una = one, feminine

It is feminine because it refers back to amigas.

If the group were masculine or mixed, you could say:

• cada uno

Because the subject of that part of the sentence is cada una, and cada una is grammatically singular.

So Spanish treats it as:

• Cada una lee... = Each one reads...

Even though the idea includes several people, the grammar is singular because you are talking about them one by one.

Because cada una is singular, and the sentence is distributing the action individually:

• cada una lee un libro diferente = each one reads a different book

So Spanish uses:

• lee = singular verb
• un libro = singular noun phrase

The meaning is not that there is only one book total. It means each person has one book, and the books are not the same.

In Spanish, adjectives often come after the noun.

So:

• un libro diferente = a different book

That is the normal order here. Placing the adjective after the noun is especially common when you are simply describing or distinguishing something.

Yes, but it would sound slightly different.

• cada una = each one
• cada amiga = each friend

Both are possible in the right context, but cada una is very natural here because the friends were already mentioned in the first part of the sentence, so Spanish avoids repeating the noun unnecessarily.

Because y means and, joining the two parts of the sentence:

• Mis amigas y yo estamos en la biblioteca
• y cada una lee un libro diferente

It works just like English and.

Spanish only changes y to e before words that begin with an i sound, and that is not the case here.

Yes.

• lee = third person singular present of leer: he/she reads
• It is pronounced with two vowel sounds: le-e

This is different from forms such as:

• leí = I read, preterite
• leé is not the standard form used in Spain for this verb form

So in the sentence, cada una lee means each one reads in the present tense.