L'adulto aspetta fuori.

Because il changes to l' before a singular noun that begins with a vowel. This is called elision.

So:

• il ragazzo
• l'adulto

The apostrophe shows that the vowel in the article has been dropped.

Here, adulto is a noun: it means the adult.

But adulto can also be an adjective, as in:

• un uomo adulto = an adult man
• una donna adulta = an adult woman

In L'adulto aspetta fuori, it stands on its own as a noun.

You can tell from the noun itself.

• adulto = masculine singular
• adulta = feminine singular

So:

• l'adulto = the adult (masculine)
• l'adulta = the adult (feminine)

The article l' can be used with both masculine and feminine singular nouns before a vowel, so the ending of the noun is what tells you the gender here.

Because Italian often drops the subject pronoun when it is clear from the verb form.

Aspetta is the third-person singular form of aspettare, so it already tells you the subject is:

• he
• she
• it
• or a singular noun like l'adulto

So Italian does not need to say lui or lei here.

Aspetta is the present tense, third-person singular of aspettare.

Its basic meaning is waits.

Depending on context, it can also be understood as:

• waits
• is waiting

So L'adulto aspetta fuori can mean either The adult waits outside or The adult is waiting outside, depending on the situation.

Because Italian uses aspettare differently from English.

In English, you usually say wait for someone.
In Italian, aspettare normally takes a direct object, with no preposition:

• Aspetto Marco = I’m waiting for Marco
• Aspettano l'autobus = They’re waiting for the bus

In your sentence, there is no object, so aspetta simply means waits / is waiting.

Fuori here means outside.

It is an adverb, and in Italian adverbs often come after the verb:

• aspetta fuori = waits outside
• mangia lentamente = eats slowly

So the word order is completely natural.

Yes. Fuori can have a few related meanings, depending on context, such as:

• outside
• out
• outdoors

But in L'adulto aspetta fuori, the most natural meaning is outside.

A simple pronunciation guide is:

l'a-DUL-to a-SPET-ta FWO-ri

A few helpful points:

• l'adulto is said smoothly, almost like one unit
• adulto has the stress on dul
• fuori is pronounced roughly fwo-ri

So the whole sentence flows as:

l'adulto aspetta fuori