1. Auschwitz was a safekeeping camp of jews, gypsies, political enemies etc.
Jews were to be deported to Madagascar. But because of Britain's blockade and the turned tide of the war, Germany couldn't deport them.
Germany's policy wasn't to kill every jew they could get their hands on, as stated in your first point, that's false.
2. Irrelevant and they didn't want to write about that. Also Churchill did express his fear over the Jew's fate.
"He had mingled in Vienna with extreme German nationalist groups, and he had heard stories of sinister, undermining activities of another race, foes and exploiters of the Nordic world - the Jews. His patriotic anger fused with envy of the rich and successful into one overpowering hate."
3. Same explanation as the first point, also there were guards.
4. It happened over 2-3 years. Many of them were shot on spot over accusations of aiding the partisans, look at the document above I posted.
The main reason of usement of the so called "death camps" was because the shooting squads began to go insane.
"my comrades and I - and I can easily say all comrades - were physically and mentally totally done after such action" (interrogation of 23 January 1962, BArch B 162/3275, p. 196).
According to Albert Hartl, head of the RSHA office IV B on ideological enemies and "visitor" of Einsatzgruppe C, the group's head Max Thomas explained that people assigned to the shooting squads developed "the worst sadistic drives" or suffered from "hysterical crying" and "health breakdown" (interrogation of Hartl of 16 January 1957, BArch B 162/1254, p. 986).
Von dem Bach-Zelewski himself suffered under a "nervous state of exhaustion" related to the "shooting of Jews supervised by himself and other heavy experiences in the East" according to a contemporary document from the Reichsarzt SS Ernst-Robert Grawitz (letter Grawitz to Himmler of 4 March 1942, Figure 3, from Bartoszewski, Erich von dem Bach, p. 97).
