Dopo le montagne russe ho le vertigini.

Because Italian normally uses the expression avere le vertigini, literally to have dizziness/vertigo, not to be dizzy.

This is very common in Italian: some physical states use avere where English uses to be. For example:

• ho fame = I am hungry
• ho sete = I am thirsty
• ho freddo = I am cold
• ho le vertigini = I am dizzy / I have vertigo

If you tried to use essere here, it would sound unnatural.

Dopo means after.

In this sentence, it is followed by a noun phrase:

• dopo le montagne russe = after the roller coaster / after the roller-coaster ride

A useful pattern is:

• dopo + noun
• dopo + infinitive structure in longer sentences, such as dopo aver mangiato = after eating

So here, dopo simply sets the time or cause of what follows.

Because le montagne russe is the normal Italian expression for roller coaster or roller coasters. It is a fixed expression and is very often used in the plural, even where English may use the singular.

Literally, it means Russian mountains, which comes from an older historical naming.

So even if English says after the roller coaster, Italian very naturally says dopo le montagne russe.

Yes, la montagna russa exists and means the roller coaster in the singular.

However, in many everyday contexts Italians still prefer the plural expression le montagne russe, especially when talking about the activity or ride experience in a general way.

So:

• la montagna russa = one specific roller coaster
• le montagne russe = roller coasters / the roller-coaster ride experience

In your sentence, dopo le montagne russe sounds very natural.

Because the normal expression is avere le vertigini, with the definite article le.

This is just how the idiom works in Italian. Not every expression with avere behaves the same way:

• ho fame = no article
• ho sete = no article
• ho le vertigini = with article

So this is something to learn as a set phrase: avere le vertigini.

In this meaning, Italian usually uses vertigini in the plural.

So the standard phrase is:

• avere le vertigini

The singular vertigine does exist, but it is not the usual form in this expression. The plural is the normal, idiomatic choice when talking about dizziness or vertigo as a physical sensation.

So for a learner, the safest thing is to memorize:

• ho le vertigini
• hai le vertigini?
• mi vengono le vertigini

Close, but not always perfectly.

Vertigini often suggests dizziness, vertigo, or a spinning/unsteady feeling. In a sentence like this, it fits very well because roller coasters can make you feel physically dizzy.

Depending on context, other Italian expressions might be used for related feelings:

• ho la nausea = I feel nauseous
• mi gira la testa = my head is spinning / I feel dizzy
• sono stordito = I feel dazed

So ho le vertigini is a very natural choice here, especially for dizziness after a ride.

Because Italian often leaves out subject pronouns when they are already clear from the verb ending.

• ho already means I have
• so io is not necessary

You could say io ho le vertigini, but that would usually add emphasis, contrast, or emotion, for example:

• Lui sta benissimo, io ho le vertigini. = He feels perfectly fine; I feel dizzy.

Without special emphasis, dropping io is the most natural choice.

Yes. Italian word order is fairly flexible.

You can also say:

• Ho le vertigini dopo le montagne russe.

That is grammatical too. The version with dopo le montagne russe at the beginning simply highlights the circumstance first: After the roller coaster, I feel dizzy.

So both are possible, but the original sentence sounds very natural because it sets the scene first.

Yes, because le belongs to montagne russe, not to dopo itself.

The structure is:

• dopo + le montagne russe

Just as you would say:

• dopo il film = after the movie
• dopo la cena = after dinner
• dopo le vacanze = after the holidays

So dopo does not remove the article. The noun keeps the article it normally needs.

Usually, in this context, it describes a temporary feeling: after riding roller coasters, the speaker feels dizzy.

But avere le vertigini can also be used more generally for vertigo as a condition, depending on context.

So the sentence itself does not force a medical interpretation. Because of dopo le montagne russe, the most natural reading is simply that the roller coaster caused the dizziness.