Learn Italian: Immagini che loro abbiano un segreto? - Do you imagine that they have a secret?

The verb immaginare (to imagine) expresses a thought, belief, or opinion. When you have a verb like this followed by che (that) and a new subject, it triggers the subjunctive mood for the second verb. Therefore, we must use the subjunctive abbiano instead of the regular present tense hanno.

Is the first verb, immagini, also in the subjunctive?

No, immagini is in the normal present tense (indicative) for the tu form. In this type of sentence, the main verb (the one doing the imagining, thinking, or doubting) stays in the normal tense. It acts as the trigger that forces the verb after che into the subjunctive.

Since abbiano can only be the 'they' form, why do we need the pronoun loro here?

You are right that abbiano is unambiguously the 'they' form, so the pronoun isn't strictly necessary to understand who is being talked about. However, Italian speakers often include pronouns like loro for emphasis or contrast. Here, it adds a slight emphasis: Do you imagine that they have a secret?

What would happen if the subjects were the same, like 'Do you imagine that you have a secret?'

When the subject of the first verb and the second verb are the same person, you don't use che and the subjunctive. Instead, you drop che and use di followed by the infinitive. It would become: Immagini di avere un segreto?