For option 2 I'll confess to not being sufficiently familiar with the gamut of what can be considered a mental illness, such that I couldn't tell you whether a person under management for such is a safer pilot than someone undiagnosed, or the median pilot. I'd be mildly surprised if you were, but stranger things have happened.
As it stands, I expect these would be the same diagnostics that until ~2013 considered sexual preferences as mental health issues.
As pragmatic rule, if one is prescribed drugs for it, one is not fit for being a pilot.
I know several people who are prescribed drugs for mental conditions. I would not get on an airplane if they were the pilot. Nor would I get on one with a pilot with a heart condition. It doesn't mean they are bad people, it's just the way it is.
Pilots who develop a heart condition get their license revoked. Every pilot knows this. There's nothing fair about that, either.
Fun fact - my Air Force dad told me that when an airplane was overhauled, the chief mechanic went up on the check ride. That ensured the job was well done.