These are basically two different questions: one asks about the clinical disease, which is thought to be syphilis from the Bonn student age.That is unimportant.
The other important question is whether he was “mentally” ill.There will always be arguments about this. For glamorous Christians, his struggle against Christianity is unacceptable. But, like Schopenhauer and Kierkegaard, he has exposed much of the mendacity of his time, and in that sense he was more serene than most of his contemporaries.
One has to see the environment: for the Catholic Church at that time democracy and especially socialism was a kind of mental illness (cf.Syllabus Errorum > Syllabus errorum – Wikipedia) So who judges how what a mental illness is?
Nietzsche was, by its very nature, a freedom-mupper who opposed all forms of substantiation — against the churches, against socialism, against the materialism of the wealthy.That is why he despised the Nazis, just as he despised his spire-like, anti-Semitic sister. That is why he later despised Wagner. Wagner had once been a Revolutionary who had to flee Germany in 1848. But instead of being like Rimbaud or like Walt Whitman or like Bizet in the opera Carmen or like the French impressionists (Manet, Monet, Renoir, etc.) for the new light and the new freedom, he served the longing of the newly rich Buergertum for Germanic-nationalist Edelkitsch in operas about the Nibelungen and Parsifal. Nietzsche was disgusted by this intellectual corruption of a man he had once worshipped.
If nietzsche wanted to be charakerized with a single word, then it would be “hunger for life and thirst for freedom”.That is why he turned his back on Schopenhauer, whose incorruptibility he continued to admire. He accused Schopenhauer only of his pessimism. Nietzsche wanted light and life, no dull Wagnerian oak-washers and no Schopenhauersche Duesternis — and also no church-moral duck-maeuserei.
So: I would describe Nietzsche as very healthy.
Nietzsche has occasionally been referred to as a proto-Nazi, referring to the ueberman and the blonde beast.These are misdeeds. The really educated under the Nazis soon realized this and left Nietzsche alone.
The uebermensch is not an SS-General, whom has been despised by Nietzsche and rather classified him among subhumans.Rather, an overhuman in the sense of Nietzsche is someone who has overturned the human swaths in himself, and thus, as superhumans, consider such as the Buddha or Socrates or Jesus. But Nietzsche agreed with Freud that the SS-General was basically a neurotic, and thus rather the opposite of an overhuman. N. says at the beginning of the Zarathustra once meaningfully that we “normal” people stand halfway between the monkeys and the “right” people. The truly free man is the target, not the SS general. That is why the title of the estate “Will to Power” won by the stupid sister is misleading. This meant the will to power over one’s own swagger, but not about “gypsies”, Eastern Europeans, gays and the disabled. As I said, Nietzsche despised and hated the Nazis. They were the opposite of what he wanted. Only his stupid sister, who was married to a fanatical anti-Semite, got bright eyes at the sight of Hitler. To her apology it must be said: She also got Heidegger. But this is a different issue.
The blonde beast is simply the Loewe, one of the three mythical figures in the Zarathustra between the camel and the child.