This is gross.
Unless you're a medical professional, please don't armchair diagnose. If you are, I'm pretty sure you were taught not to diagnose mental illness of celebrities without meeting them, as all medical folks I know personally have told me they were taught.
That is indeed what is taught, but first up, some things are just so obvious that you don't actually have to examine anyone to "diagnose" correctly. Second, we are talking about the most powerful man on earth, so this is not just meanspirited gossiping, this is actually important and a vital interest to the public.
For the record I am a psychologist, although for the last decade and a half I have taught psychology and political science instead of practising psychology.