Very interesting questions... The ancient Egyptians knew about mental illness a few thousand years B.C. and CAT scans of mummies show they did brain surgery by drilling a hole through the skull, which the scans often showed healed (meaning the patient survived long after surgery). The ancient Greeks and Romans also knew of mental illness and had elaborate descriptions of it and explanations for it, and I believe the Chinese knew of mental illness thousands of years ago also, though my Chinese history is limited.
I'm not sure what the "first" mental illness discovered was or who precisely discovered it, but it's been around in people and other animals, and known about, for thousands of years according to the reading I've done over the last 17 years--I doubt anyone can specifically answer either question because new archaeological discoveries occur frequently, upsetting the history books. :-)