I can only address one sliver of your question. Perhaps other experts will add their own knowledge.

The Vatican viewed Hitler with growing suspicion and unease between his ascent to power and the outbreak of war. The main figure in this period of Vatican history is Pope Pius XI, and of secondary importance was Cardinal Secretary of State Eugenio Pacelli. The first important interaction between the two parties was the signing of the Reichskonkordat in 1933. The violations of the concordat began almost immediately, and there were dozens of papal protests between 1933 and 1939 that fell on deaf ears in Berlin.

At first, the various fascist movements were seen as useful tools against the threat of communism in Europe. However, living alongside fascist governments soon proved that there were a number of problems. Aggressive fascist rhetoric about the primacy of the state and rampant racist claims became more and more troubling for the papacy. In March of 1937, Mit Brennender Sorge was shipped to every Catholic church in Germany via motorcycle courier.

The first part of the encyclical deals with condemning Nazi violations of the Reichskonkordat, signed in 1933. The remainder deals with outlining the problems the Church had with Nazi ideology. Perhaps the most striking excerpt comes from section 8:

Whoever exalts race, or the people, or the State, or a particular form of State, or the depositories of power, or any other fundamental value of the human community - however necessary and honorable be their function in worldly things - whoever raises these notions above their standard value and divinizes them to an idolatrous level, distorts and perverts an order of the world planned and created by God; he is far from the true faith in God and from the concept of life which that faith upholds.

Sections 15 and 16 praise the Old Testament, an oblique statement of support for German jews. This becomes more explicit in section 18:

The Church founded by the Redeemer is one, the same for all races and all nations. Beneath her dome, as beneath the vault of heaven, there is but one country for all nations and tongues; there is room for the development of every quality, advantage, task and vocation which God the Creator and Savior has allotted to individuals as well as to ethnical communities

Another explicit refutation of the ideology of race is present in section 11:

None but superficial minds could stumble into concepts of a national God, of a national religion; or attempt to lock within the frontiers of a single people, within the narrow limits of a single race, God, the Creator of the universe, King and Legislator of all nations before whose immensity they are "as a drop of a bucket" (Isaiah xI, 15).

The call to action by individual Catholics is in section 19, "at no moment of history, no individual, in no organization can dispense himself from the duty of loyally examining his conscience, of mercilessly purifying himself, and energetically renewing himself in spirit and in action." It is clear, sadly, that many Catholics had divided loyalty and did not heed the call to heroism in section 21. Far too many chose country over Church in this instance, and many Catholics participated in the atrocities of WWII.

In the wake of the publication of the encyclical, Vatican radio was banned in Germany and Catholic newspapers were shut down. Pius XI died in February of 1939, leaving his successor to deal with WWII. That successor was the same Eugenio Pacelli mentioned at the beginning of this post—the man who is also the subject of my flair here on /r/Askhistorians.

As always, followup questions by OP and others are always welcome!