There are a lot of questions here, not all of which I can answer, so I'll go with what I know. There will be a lot missing, so I'll have to beg your pardon.

Regarding when the knowledge of the "full extent" of the Holocaust to reach the "American public". There are many things we need to unpack before we can even begin to answer this question. What is the "full extent" of the Holocaust? For a very long time, there was this notion that the Holocaust was committed primarily by the SS and that it was primarily committed in camps. This is simply not the case however. The seminal work that disproved this was Chris Browning's 1992 book Ordinary Men, which convincingly argued that reserve police battalions - literally ordinary cops, not SS fanatics - were at least partially responsible for the open air killings that made up the majority of killings in the first part of the war in Poland and Russia. One could also argue that we are still learning about the Holocaust to this day. The United States Holocaust Memorial Museum in Washington spends hundreds of thousands, if not millions, of dollars every year on research on the Holocaust.
Further, there is the question of the American public. What percentage of the American public counts as enough? There are, no doubt, lots of folks who are at least vaguely aware of camps like Auschwitz and that Hitler tried to kill the Jews. Would that knowledge count? I would venture that most laymen are unaware that at least half of the Jews killed during the Holocaust were shot in the open air, and pushed into mass graves. In a highly controversial (for reasons not relevant here) work, Daniel Goldhagen convincingly argues in his work Hitler's Willing Executioners that the Holocaust was not actually a case of modern industrial genocide, as most laymen probably believe, but rather very efficient killing by traditional methods. I've already mentioned the open air killings, but even in the gas chambers were not terribly industrial. Many people, because of the movie Schindler's List, are familiar with the showers. But most people aren't aware that the gas was actually just pellets that were dropped in through vents in the ceiling. It wasn't pumped through the shower heads at all. That's not very industrial at all. Now granted, some gas chambers and the mobile killing vans did use CO2 to suffocate their victims, but that is a minority.
The point I'm bringing up here is that one could argue that the "full extent" of the Holocaust is still not known by the majority of the American public. To say the least, much of this comes as a shock to my students.

But getting beyond quibbles about the "full extent" of the Holocaust, you're probably asking about when the basic outlines of the genocide plan were at least understood to be real, as opposed to some sort of anti-German propaganda. Certainly by the end of the war, when Eisenhower forced his troops, along with German civilians, to tour some of the concentration camps with the express intent of heading off later possible denial of the killings. But even before that, as early as 1942, reports had made it back to the US about the killings. The New York times ran a story in July 1942 about the killing center at Chelmno. There was knowledge available to those who were willing to find it. Now how many people read that story or fully comprehended what it meant is another question entirely, but the information was there to be known. The desire not to believe should not be underestimated. Even some Jews could not fathom the genocide, as is evidenced in Elie Wiesel's semi-autobiographical historical novel Night.

Regarding the teaching of the Holocuast in American schools. This is a much more recent phenomenon, dating, mostly, to the late 1980s and 1990s. I would go into more detail, but my wife just got home and I need to get off the computer - sorry. Check out the Holocaust Education Foundation at Northwestern University for more info. Started by survivor Zev Weiss, I got most of my info on Holocaust Education from attending seminars sponsored by this group. Also, USHMM has great online resources regarding the basics of this question - i.e. who knew what and when.