I have answered some related questions here in case you want to read them, but I will answer your question a bit more directly as well.

I do not have the answer to everything in your question, but I can give some context and clarity. I believe.

Much of German theology of the early Twentieth Century was Liberal Theology. This meant, generally, that it did not view scripture as the Holy and revealed word of God. Instead, scripture is understood as the views on God of the author at the time of its writing. Hence, we can understand the intellectual/theological progression of Jews-->Christians in scripture. From this we can create general understandings of Christian principles and ideals; however, it scripture cannot garner specific, unerring "truths."

Liberal theology was decried by conservative German theologians in the late Nineteenth century. Additionally, it was associated with liberal political thought. Therefore, conservative German theology allied with Conservative German politics. Hence, numerous conservative Lutheran scholars of the period upheld the importance of the state (read monarchy) to maintain order and morality. Liberal politics were associated with immorality (even atheism).

Ironically, by the 1920s, most German theologians were liberal in their view of scripture, but conservative in their view of politics. They viewed the Weimar Republic as dangerous to the moral and spiritual development of the German people. Its socialism was associated with atheism and its liberal social policies were connected to moral degeneration. Many theologians, for example Paul Althaus, believed that Germany needed a sort of regeneration. This was delivered, according to them, in 1933.

Paul Althaus and another liberal theologian Emanuel Hirsch, with their denial of scriptural authority, found a new authority...the German volk. They began to suggest that the the good of the German people itself was an authority from God. Hirsch added to authorities of family, government, and profession, the even greater authority of volk. Indeed, both believed that Christian nature was revealed in the German volk. In their morality and order. When the National Socialists held up German order and morality as important values, many German theologians went along with it.

Althaus went so far in this theological system as to state that "“Our life in our Volk is not our eternal life; but we have no eternal life if we do not live for our Volk.” (translated in Theologians Under Hitler by Erickson).

Ultimately, and to more clear attempts to answer your questions...

German theologians were liberal and on the cutting edge of Biblical criticism. They denied the authority of scripture.

Positive Christianity was more related to other authorities than scriptural ones, although its proponents did appeal to scripture through their volkisch lens. They usually read out anything related to Jesus as a Jew and other things of Jewish orientation.

Karl Barth wrote the Barmen declaration (a foundational document for the Confessing Church) in 1934 and in 1935 lost his professorship at the University of Bonn for his refusal to swear an oath to Hitler. Dietrich Bonhoeffer certainly opposed the Nazis, held an underground seminary for the Confessing Church, and was executed in the last days of the regime. Martin Niemoller, originally supported the Nazis but became a leader of the Confessing Church. Neo-Orthodox theologians tended to be more resistant than liberal theologians.

As the above demonstrates, the University professors were required to swear an oath to Hitler. They did not, however, have to espouse Positive Christianity. This is because the church was one of the few aspects of society that did not become completely "nazified."