There is an excellent timeline of the Holocaust, and its reporting to the Allied nations, at:
Timeline | American Experience | Official Site | PBS
It notes that the first press reports of massacres of thousands of Jewish civilians in western Russia surfaced in July of 1941.
In May of 1942, Polish Resistance workers transmit to London a document summarizing Nazi massacres of Jews in Poland and Russia
A press conference held by the World Jewish Congress in London on June 29th, 1942, estimated that over a million Jews had been killed by the Nazis.
The first word of an official Nazi policy of total annihilation of the Jews in Europe comes from Switzerland in August of 1942.
(Above notes from the PBS “American Experience” page).
As Reality Chuck noted, many in the public took the figures, and even the reports, with a grain of salt; the Allied (and in particular the British) propaganda machine of World War One had been extremely successful in spreading stories of German “frightfulness,” the vast majority of which were false. After WWI, many took such atrocity reports to be exaggerated, or even false.
The first public mention of the word “holocaust” that I have seen personally in a primary source is in a Winnipeg, Canada Jewish organization’s quarterly yearbook from mid-1943. Even so, IIRC, most of the text talks in terms of “many thousands” being killed and sent to concentration camps (although this referred, I believe, to the Warsaw Ghetto and Theresienstadt rather than the death camps).
How much the German public knew is a tricky question. Many, I believe, just didn’t want to know; an elderly German of my acquaintance (who would have been in his early 40s in 1940) once told me that he remembered civilians making reference to troublemakers (in the sense of people criticizing the regime) “going up the chimney,” if they didn’t watch their step. An interesting reference is Gitta Sereny’s excellent book “Into that Darkness,” the story of Franz Strangl, commandant of Treblinka, and also the development of the Nazi gassing program, beginning with “mental defectives,” which laid the groundwork for the later death camps.
Sereny quotes one man (interviewed afer the war) about knowledge of the Holocaust:
Ian Kershaw, in his book “Popular Opinion & Political Dissent in the Third Reich,” makes particular mention of the protests in Bavaria over the Nazi euthenasia of mental patients and disabled, but notes the complaisance over the transportation of Jews from Bavaria.
I will try to add more to this later, addressing the last 3 questions on the OP, but for now I have to go to work.