Nietzche, anti semitism and national socialism

What was nietzches relation to anti semitism and nazism?

Reason being... well there are many motivations: 1. I read a passage from the geneology of morals... he did not exactly express great love for jewish culture, to put it that way. He did express great admiration for the Aryan, the blond beast of prey. Also mentioned how the German people had degraded since trough time due to… jews 2. I once read a book called Nietzche and the nazis. The details are fuzzy, as its so long since I read it, but the argument was that he was a huge inspiration for the movement and german people between 1918-1945. 3. There are claims that his cousin or some female relative edited his writings to be anti sematic, is there any truth to this? 4. As a self proclaimed immoralist* you subscribe to might makes right, correct? That is a facist belief as well, is it not?

* People have never asked me as they should have done, what the name of Zarathustra precisely meant in my mouth, in the mouth of the first immoralist; for that which distinguishes this Persian from all others in the past is the very fact that he was the exact reverse of an immoralist. Zarathustra was the first to see in the struggle between good and evil the essential wheel in the working of things. The translation of morality into the realm of metaphysics, as force, cause, end-in-itself, is his work. But the very question suggests its own answer. Zarathustra created this most portentous of all errors,—morality; therefore he must be the first to expose it. Not only because he has had longer and greater experience of the subject than any other thinker,—all history is indeed the experimental refutation of the theory of the so-called moral order of things,—but because of the more important fact that Zarathustra was the most truthful of thinkers. In his teaching alone is truthfulness upheld as the highest virtue—that is to say, as the reverse of the cowardice of the "idealist" who takes to his heels at the sight of reality. Zarathustra has more pluck in his body than all other thinkers put together. To tell the truth and to aim straight: that is the first Persian virtue. Have I made myself clear? ... The overcoming of morality by itself, through truthfulness, the moralist's overcoming of himself in his opposite—in me—that is what the name Zarathustra means in my mouth.

— Ecce Homo, "Why I Am a Fatality"