How come some of the Nazi leadership were pagans or practiced occultism and mysticism despite most of Germany being Christian? Did Hitler seek such men out? Was there a plan to erradicate Christianity in Germany and replace it with such beliefs? What did German citizens think of all this?

To put it bluntly, the influence of this is vastly blown out of proportion in pop culture because it makes for a good story.

Such as it was, the occult influence on the leadership of the Reich was confined to a small circle within the higher ranks of the SS - Himmler certainly had some strange ideas, but outside of a small circle it was mostly theatrical window dressing. In fact, the Reich actively campaigned against Occultism in society and imprisoned members of the Freemasons, the OTO and other occult groups.

Hitler himself publicly rebuked the tendency towards mysticism in a speech in 1936: "We have nothing to do with those elements who only understand National Socialism in terms of hearsay and sagas, and therefore confuse it too easily with vague Nordic phrases and who are now beginning their research based on motifs from some vague Atlantean culture. National Socialism sharply dismisses this sort of culture."

This speech was alluding to the sacking of one Herman Wirth as head of the Ahnenerbe - the "Ancestral research institute". As the Speech implies, the Ahnenerbe did have some very odd pseudo-scientific and occult ideas, and it is this organization from which the pop-culture trope of "Occult Nazis" flows in most part. It was essentially a pet project of Himmler to uncover the "hidden history" of the Aryan race by sending research teams to far-flung locations in order to take fiend recordings, photographs, cranial measurements and the like to prove that great civilizations of the world were Germanic in origin. It's an interesting story in itself with some truly odd characters - Wirth, Otto Rahn, Karl-Maria Willigut and so forth. But it was a small operation and not reflective of party policy.

The relationship between the Churches and the Nazi state is an interesting question in itself. While Hitler certainly did not approve of a politically active Church system, either Protestant or Catholic, he always stepped lightly around directly confronting them. In fact, the policy of not directly antagonizing the churches is behind the rebuke to the Ahnenerbe I mention above.

Sources:

The Occult roots of Nazism. Nicholas Goodrich-Clarke

The master plan: Himmler's scholars and the Holocaust. Heather Pringle

The secret King: Karl Maria Willigut, Himmler's master of the runes. Michael Moynihan & Stephen Flowers