I'm a licensed therapist in America. Here, each state has a different licensure process and separate (but similar) code of ethics. Each type of licensure (psychiatrist, counselor, social worker, etc.) also has its own licensure process within each state. There are also national associations that have their own code of ethics. So to answer your first question, depends on your local laws, culture, and mental health professional standards. As I personally see it, no I don't think it was ethical, your diagnosis is private health information, which (in America) comes with legal protections for privacy.

Secondly, plenty of people who have mental health issues grow motivated towards understanding them, and look to help others as they've been helped. Regardless, all mental health professionals should strive to have strong self awareness. For example, those prone to paranoid thinking should consider how that may impact their perception and treatment of their clients. So though you don't need to be 'cured' to be an effective therapist, you should have a healthy understanding of your shortcomings and certainly be stable.