Aspetto il mio amico fuori dalla biblioteca.

In Italian, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• Aspetto = I wait / I am waiting
• The -o ending tells you the subject is io

So Aspetto il mio amico is completely natural.
You can say Io aspetto il mio amico if you want extra emphasis, contrast, or clarity, but in normal speech the io is usually unnecessary.

Aspetto is the present tense of aspettare.

In Italian, the present tense often covers both ideas that English separates into:

• I wait
• I am waiting

So in this sentence, Aspetto il mio amico is naturally understood as I am waiting for my friend, depending on context.

In standard Italian, possessives usually take the definite article.

So:

• il mio amico = my friend
• literally: the my friend

That sounds strange in English, but it is normal in Italian.

A few notes:

• With most singular family members, Italian often drops the article:
  mio fratello, mia madre
• But amico is not a family term, so the article stays:
  il mio amico

Dalla is a combination of:

• da = from / by / at, depending on context
• la = the

So:

• da + la = dalla

After fuori, Italian normally uses di or da depending on meaning and structure. In this sentence, fuori dalla biblioteca means outside the library.

You can think of it as:

• fuori da
  • place = outside of / outside

So:

• fuori dalla biblioteca = outside the library

No, not in standard Italian for this meaning.

To say outside the library, you need the preposition:

• fuori dalla biblioteca

Without da, fuori la biblioteca would sound incorrect in standard Italian.

The fixed pattern to remember is:

• fuori da + place
• fuori dal cinema
• fuori dalla scuola
• fuori dall’ufficio

This is a very common point for English speakers.

• biblioteca = library
• libreria = bookshop / bookstore

So if you want to say library, biblioteca is the correct word here.

This is an important false friend because libreria looks a lot like library, but it usually does not mean that.

Italian normally uses the definite article with many nouns where English may also use the, and in prepositional phrases the article often combines with the preposition.

Here:

• la biblioteca = the library
• da + la biblioteca becomes dalla biblioteca

This is called an articulated preposition: a preposition joined with a definite article.

Other examples:

• a + il = al
• di + il = del
• in + i = nei
• da + la = dalla

The given order is the most neutral and natural:

• Aspetto il mio amico fuori dalla biblioteca.

But Italian word order is somewhat flexible, especially to change emphasis.

For example:

• Fuori dalla biblioteca aspetto il mio amico.
  This puts more focus on the location.
• Aspetto fuori dalla biblioteca il mio amico.
  This is possible, but less neutral and may sound marked depending on context.

So yes, the order can change, but the original sentence is the safest and most standard version.

Then the noun, article, and possessive change to match the gender:

• Aspetto la mia amica fuori dalla biblioteca.

Compare:

• il mio amico = my male friend
• la mia amica = my female friend

The possessive must agree with the noun it goes with:

• mio with masculine singular nouns
• mia with feminine singular nouns

By itself, amico normally means friend.

So:

• il mio amico usually means my friend

If someone wants to clearly say boyfriend, Italian more often uses:

• il mio ragazzo

Likewise:

• la mia amica = my friend
• la mia ragazza = my girlfriend

Context matters, but in a basic sentence like this, il mio amico is understood as my friend.

Context decides that, but in this sentence the natural meaning is outside the library.

Because the whole sentence is:

• Aspetto il mio amico fuori dalla biblioteca.

This describes where the speaker is waiting, so fuori dalla biblioteca works as a location: outside the library.

If the idea were movement from inside to outside, the surrounding context would usually make that clearer. Here it is simply the place where the waiting happens.