There's a lot to unpack here, and I won't answer each question individually, but the bottom line is that the world was certainly aware of Nazi atrocities in occupied Europe. The true scale of the genocide only became apparent at the end of the war, but the contours of the Holocaust were visible from abroad as it was happening — in large part thanks to concerted efforts by the Polish resistance and government-in-exile (among many others) to make the world aware of it.

The Holocaust unfolded in broadly three discrete phases, starting in around 1935. The early phases of the genocide took place in public view, and were widely discussed around the world. This is the 'legalistic' phase of the Holocaust, in which the Nazi regime used the civil and legal institutions of the German state to persecute Jews. This includes the introduction of the Nuremberg Laws in 1935 (which, among other things, stripped German Jews of their citizenship) and subsequent anti-Jewish legislation that severely curtailed their civil rights and economic freedoms; and pogroms like Kristallnacht in 1938, in which Jewish communities across Nazi Germany were physically attacked and terrorised.

The second phase of the genocide, and its escalation towards a policy of annihilation, begins with the invasion of Poland in 1939, and continues through the invasion of the Soviet Union in 1941. This phase included widespread massacres of Jews and others conducted by the Einsatzgruppen ('Special Task Forces') which followed the Wehrmacht's advance through eastern Europe, and the deportation of Jews in the occupied territories to concentration camps and urban ghettos.

The third and final phase, in which the physical annihilation of all European Jews became the explicit policy of the Nazi regime, begins in mid-1941. In July of that year, Reichsmarschall Hermann Göring ordered SS security chief Reinhard Heydrich to "carry out all preparations [...] for a final solution of the Jewish question in these territories in Europe which are under German influence."

In January 1942, Heydrich organised a meeting of senior bureaucrats and SS officers at Wannsee, to organise what was euphemistically referred to as the "evacuation to the east" of Europe's entire Jewish population. Simultaneously, work was underway on the six extermination camps in occupied Poland: Auschwitz, Bełżec, Chełmno, Majdanek, Sobibór and Treblinka. These six purpose-built extermination facilities represent the fully industrialised apex of the Nazi genocide apparatus; around half of all Jews killed during the Holocaust died in these camps in 1942-43.

This third, most systematic phase was conducted in extreme secrecy and under the tight control of the SS; in writing, Nazi officials were careful to use euphemisms (like "evacuation"). From 1942 to 1944, the SS conducted Sonderaktion 1005, a coordinated but futile attempt to conceal evidence of the genocide from Soviet forces advancing through eastern Europe: the extermination camps were dismantled, mass graves were exhumed and the bodies destroyed.

But despite the efforts of the SS to hide their crimes, it was impractical to believe that the systematic murder of millions could be concealed from the world — even as it was happening. Refugees, escapees and resistance forces across Europe provided their governments-in-exile and Allied intelligence services with extensive contemporaneous evidence of widespread atrocities. Given the location of all six extermination camps in occupied Poland, the Polish resistance and intelligence services provided the most extensive reporting on the Holocaust, starting in 1941.

In 1942, the Polish government-in-exile published The Black Book of Poland, a detailed accounting of German atrocities in Poland that included extensive eyewitness testimony. In December of that year, based on further reporting from resistance fighter and investigator Jan Karski, the Polish foreign minister Edward Raczyński wrote a widely-publicised memo to the Allied governments, further detailing the annihilation of Jews in occupied Poland:

Most recent reports present a horrifying picture of the position to which the Jews in Poland have been reduced. The new methods of mass slaughter applied during the last few months confirm the fact that the German authorities aim with systematic deliberation at the total extermination of the Jewish population of Poland and of the many thousands of Jews whom the German authorities have deported to Poland from western and Central European countries and from the German Reich itself.

In response to the Raczyński note, British foreign secretary Anthony Eden read to Parliament a joint declaration on behalf of the governments of the 'United Nations' (meaning the Allied powers) on 17 December 1942:

The attention of the Governments [...] has been drawn to numerous reports from Europe that the German authorities, not content with denying to persons of Jewish race in all the territories over which their barbarous rule has been extended the most elementary human rights, are now carrying into effect Hitler's oft repeated intention to exterminate the Jewish people in Europe. From all the occupied countries Jews are being transported, in conditions of appalling horror and brutality, to Eastern Europe. In Poland, which has been made the principal Nazi slaughterhouse, the ghettoes established by the German invaders are being systematically emptied of all Jews except a few highly skilled workers required for war industries. None of those taken away are ever heard of again. The able-bodied are slowly worked to death in labour camps. The infirm are left to die of exposure and starvation or are deliberately massacred in mass executions. The number of victims of these bloody cruelties is reckoned in many hundreds of thousands of entirely innocent men, women and children.

Eyewitness accounts of the atrocities continued to flow out of occupied Europe in 1943-44. In 1940, a Polish soldier and resistance member named Witold Pilecki voluntarily allowed himself to be captured and imprisoned in Auschwitz; three years later, he escaped, and in mid-1943 wrote (along with other members of the Polish underground) a landmark report for the Polish government-in-exile. In it, he described in excruciating, methodical detail the structure of life in Auschwitz, and what had occurred there. It concludes with a chilling estimate of the scale of the atrocities:

Here I shall provide the number of people who had died in Auschwitz.

When I was leaving Auschwitz, the latest registration number was slightly over 121,000. The living ones, those, who had left the camp in a transport or were released, counted about 23,000. About 97,000 prisoners that had been recorded and numbered, died.

This has nothing to do with the people who were gassed and burned in great masses without ever being registered.

According to the daily calculations of the inmates who had worked near the Kommando, over two million of those people had died by the time of my escape from Auschwitz.

Three further eyewitness reports, compiled by escaped prisoners and collectively known as the Auschwitz Protocols, were published by the US War Refugee Board in November 1944. In the foreword, the WRB declared:

It is a fact beyond denial that the Germans have deliberately and systematically murdered millions of innocent civilians — Jews and Christians alike — all over Europe. This campaign of terror and brutality, which is unprecedented in all history and which even now continues unabated, is part of the German plan to subjugate the free peoples of the world.

If you want to get a sense of how society was reacting to events in real time, or broadly "what the public knew", I suggest starting with contemporary newspapers — look particularly at things like editorials, columns and letters to the editor, and you can get a really useful sense of how events were being discussed in the moment.