Only what the doctor(s) ask for. I made the mistake of being too talkative about my disorder. A lot of my illness is better kept private. The doctor(s) only really need to understand that I am experiencing symptoms & the casual scientific events of my disorder - not the specifics, such as conversations I’ve had with the characters/voices or what they look like, what I believe, etc.
I don’t think there are such things as “false” beliefs. Beliefs are really just convinctions of unknown things in the super or supra natural world. Everyone has beliefs. It’s the ones about the “real world”, such as that you are being monitored by the CIA, stalked, hunted, etc. are the ones you need to examine and get rid of.
Essentially, there are “false” beliefs about the real world, but don’t let anyone take away your belief system of a potential world beyond this one - such as a spiritual belief system.