Learn French: Il est possible qu'il ait partagé la confidence. - It's possible that he shared the secret.

The phrase Il est possible que expresses doubt or uncertainty, which triggers the subjunctive. Because the action of sharing the secret already happened (it is in the past relative to the present possibility), we need the past subjunctive. It is formed using the present subjunctive of the auxiliary avoir (ait) plus the past participle (partagé).

Would I still use the subjunctive if the sentence started with Il est probable que?

Usually, no! This is a classic trap. While il est possible que (it is possible that) expresses enough doubt to require the subjunctive, il est probable que (it is probable that) expresses a high degree of certainty in French and takes the indicative (like qu'il a partagé).

La confidence looks like the English word "confidence", but it is translated as "secret" here. Are they false friends?

Yes, mostly! In French, une confidence specifically refers to a secret, a private matter, or a confession entrusted to someone. If you want to talk about "self-confidence" in French, you would use la confiance en soi.

Does the past participle partagé ever need to agree with la confidence since it is feminine?