Should I write to my ex's psychiatrist?

I would not do that. It would be unethical and inappropriate for the psychiatrist to take it into consideration. There are HIPPA laws in place to prevent this from happening. I am wondering why you are so involved in the mental treatment of your ex?? If he broke it off to deal with his problems, let him do that. He needs space. For someone who suffers from a mental disorder (and I'm writing purely from personal experience) it is offensive and invasive for someone to try and interfere with their treatment or therapy. I would resent someone for that.

As far as him not being truthful about his background....Your perception is your reality....therefore his perception is his reality. If there are things he is not willing or wanting to talk about that is his decision. You can't put it upon yourself to fix him. It will never work. He may end up hating you for it. I know you may want to help but the best thing you could probably do is give him time and space.

You're an ex. Mind your own business and move on with your life.

It's in appropriate and none of your business

id think it matters alot how sever this info is leik did he kill someoen or sexuall assault or attack someoen without that ? if it isnt seriosu i woudlnt write it. but if it is soemthing terible liekt hat then yes abusiveness yes