Learn Italian: Non si fidano più e si separano. - They no longer trust each other and they separate.

Si is usually the reflexive pronoun for "himself," "herself," or "themselves." But when used with plural verbs like fidano and separano, it often expresses a reciprocal action, meaning the subjects are doing the action to each other. So, si fidano means "they trust each other."

How does the phrase non ... più work here?

Non ... più is a common pair that means "no longer" or "not anymore." In Italian, non goes before the verb and its pronoun (si), while più goes immediately after the verb. Together, they wrap around the verb phrase: non si fidano più (they no longer trust each other).

If the dictionary verb is fidarsi, why isn't there a di (of) in the sentence?

The verb fidarsi usually requires the preposition di when you state who is being trusted (for example, si fidano di te means "they trust you"). But because the action here is reciprocal, the "who" is already covered by the "each other" pronoun si. You don't need di unless you are pointing to an outside object.

Is separano used differently in Italian than "separate" is in English?