“The division into West and East was a punishment for World War II”
Germany and, in turn, Berlin underwent an administrative division into four zones/sectors at the end of the war, which was an outcome of the agreements between the allies and not yet a twofold division into West and East. The latter only took place much later on, turning the administrative division into a political division, which was not foreseen in any of the agreements - in fact, the political division into West and East was an outcome of disagreements between the allies. It was not a punishment for World War II but a result of the Cold War.
“The Soviets violated the agreements”
The construction of the centerpiece of the Berlin Wall in 1961, which turned a political division into a physical border, was indeed a violation of the original WW2 agreements. However, those agreements had already been violated before - in fact, the US (followed by the UK and France) violated the very same agreements in 1948 with the introduction of a new currency (the D-Mark), to which the Soviet Union reacted with the Berlin Blockade, that ultimately failed. The Western allies violated the same agreements again by imposing the creation of a new state, the Federal Republic of Germany (a.k.a. West-Germany) in May 1949, to which the Soviet Union reacted with the creation of the German Democratic Republic (a.k.a. East-Germany) half a year later, in May 1949. As long as the Soviet Union didn't have nuclear weapons, the Soviets couldn't really prevent any of this, but only react in hindsight. So really, both sides violated the agreements, and the Soviets weren't the first.
“People were starving in East Germany”
Although the economic gap between West and East Germany increased over time, East Germany's economy was actually doing much better than any other communist country (with the exception of contemporary China, which can hardly be described as communist by now). East Germany was eventually exporting goods to many countries, including Western markets. It even had its own high-tech industry, necessitated by the American embargo on importing computers to the communist block. Their computers were only 5-10 years behind, which is quite astonishing considering the circumstances. Historically speaking, people never lived better in the territory of the GDR, at any era before the GDR, as they did during the GDR - in material terms (excluding other aspects such as political freedom).
“Nobody could have known about the Holocaust”
It is very hard to speak in very decisive, black-or-white terms. It's also very hard to define what it is, exactly, that people could or would or should have known about in terms of the Holocaust. Nevertheless, given the immense, unprecedented magnitude, it would not have been possible to keep that a secret. Specifically in Berlin, whence about 55,000 Jews were deported, it is quite impossible that nobody would have noticed their disappearance. So even if people wouldn't have had in real-time the kind of knowledge we have in hindsight, it's very unlikely they wouldn't have known anything - ultimately, it's all about the gray zone, making generalizations impossible such as “nobody could have known”.
“Everybody knew about the Holocaust”
As noted above, it is very hard to speak in very decisive terms, so this opposite statement is just as difficult as the former one. The term in itself is a retrospective, which can be broken down into different real-time aspects of what we refer to as “The Holocaust”. Would ordinary Berliners have known about specific places such as Sobibor or Treblinka? Probably not. Could they noticed their neighbors being kidnapped? Probably yes. Would have heard their relatives, having returned home as soldiers for Christmas, talking about mass shootings? That depends on their relatives. The questions about real-time knowledge of the Holocaust really depend on what exact aspect of the Holocaust one is talking about, what level of knowledge and among what kind of people. But ultimately, one way or another, it is bound to end up in the gray zone.
“People in East-German were very poor”
Sometimes people imagine life behind the wall along the lines of contemporary Venezuela or even North Korea. It is of course true that material standard of living was lower in East Germany than in West Germany - while both parts had to make up for the destruction during the war, West Germany could rely on American funding (the Marshall Plan), while East Germany had to provide reparations to the USSR, making things even worse. Over the four decades of the German division, the gap between the two countries became wider. Yet East Germany did much better than any other communist country and was, eventually, able to substantially improve its citizens' living conditions. In fact, one could say that while the economic progress in East Germany was never has fast as in the West, it was nevertheless on a higher level than ever before in its territory. For example, housing and medicine in East Germany were better than ever before, although often not as good as in West Germany. East Germany even had its own computer industry with a delay of 5-10 years behind the Western market standard - considering the (communist) circumstances, that was quite an achievement.
“Religion was forbidden in Communism”
Many Americans think about the Soviet version of communism as the only kind of communism, but actually, there's no one “official” kind of communism. As prominent as the Soviet Union was for the communist world, the idea didn't begin there - its visionaries Karl Marx and Friedrich Engels came from Germany. East Germany or the “German Democratic Republic”, as it called itself, was a different state with a different system than the USSR. Specifically in terms of religion, the East German version of Communism was very different than the Soviet version. While in the Soviet Union, religion was persecuted in ways that were sometimes incredibly harsh, East Germany went a different way: Religious communities were indeed observed by the security service, but their work was not only legal, but actually supported and even financed by the state. This is, in fact, why and how Angela Merkel came to East Germany: She was born in West Germany, but her father, a minister, wanted to make a contribution to the communist vision by moving voluntarily to East Germany and working there as a government-employed protestant minister.
“German Jews were totally integrated into the German society”
While Jews were highly over-represented in certain fields such as law, medicine and business, most Jews were not at the top, but simply middle or working class. More importantly, every coin has two sides, and integration is never just about one's self-perception, buy always and necessarily about one's perception by the rest of society. Truth be told: There was never a time in Germany's modern history in which the “Jewish Question” was not debated. In other words: There was never a "Golden Age" in which the self-perception of Jews as Germans was obvious and unquestioned. The desire to belong, combined with the lack of appreciation by society as a whole, created the need to over-compensate and many Jews became hardcore patriots, acting even more German than the Germans. But they were never integrated so much for their new identity to truly become a matter of course.
“Hitler personally ordered the Holocaust”
People tend to make history a very personal thing, probably because it is easier to understand historical developments by making it about someone and turning it into a personal drama, like in a movie. This way, complex matters can be understood faster than with abstract terms and notions. But unfortunately, there's no evidence for a direct top-down order by Hitler. If there was an order, it would have likely been an oral one. In fact, many historians actually dispute the whole top-down model in favor of a bottom-up explanation: During the first decades after the war, many historians (now called “intentionalists”) thought about the Holocaust as the direct outcome of a clear intention to kill all the Jews since the very beginning of the Nazi regime. Since the 1980s, however, historians tend to explain the Holocaust as the work of lower ranking people during the war, whose decisions and actions were probably approved by Hitler in hindsight (these historians are called “functionalists”). You can read more about this debate on Yad Vashem's website.
“Hitler was Jewish himself”
While there is no evidence of Hitler having had some “Jewish blood”, there is also no evidence that he didn't have any. Confused? So was Hitler, it seems. The rumors about his alleged Jewish background were circulating in real-time, while he was campaigning. Once in power, he sent one of his most trustworthy men, Hans Frank, to discover the truth. Later on, Frank became the infamous “Butcher of Poland” and was eventually executed in Nuremberg. During his trial, Frank found some redemption in Catholicism, expressed remorse, and provided evidence for his own conviction. There is, therefore, little reason to doubt the story about his mission to find proof of Hitler's “pure Aryan” background. In his memories, which he wrote in prison awaiting his execution, he tells that he couldn't find any proof at all - be it about Hitler having some “Jewish blood” or not having any. But, he says, there was no way he could come back to Hitler with such a result. It was after all Hitler himself, obsessed with doubt, who sent him on this mission to begin with. Thus, Frank returned claiming it is absolutely certain that Hitler has no Jewish blood. Frank concludes this story with the correct psychological question: Regardless of the truth, can anyone imagine what such doubt might have caused in Hitler's psyche?
“The new Germany has abandoned its ethnic origin to include people from many different backgrounds"
While Germany has indeed become very diverse with about 25% of its population having some kind of background as immigrants, it is still based on the idea of a nation-state for the Germans as an ethnic group and even has a Law of Return that's very similar to the Israeli concept regarding Jewish peoplehood. The German law allows people of German ethnicity, whose ancestors left Germany many centuries ago, to “return” to their ancestral fatherland. In recent decades, millions of people have “made Aliyah” to Germany this way - mainly ethnic Germans from different places in Eastern Europe, to which they ancestors had migrated centuries ago.
“Germany has learned a lot from its history and is a true friend of Israel"
If you follow Germany's votes in the UN, you will see that in all Israel-related matters, the German vote will almost always be the exact opposite of the American vote. When America votes "No" on anti-Israeli resolutions, Germany will almost always vote "Yes" , which placed the German UN ambassador on the Simon Wiesenthal Center's list of Worst Antisemites in 2019. In fact, Germany cultivates a warm relationship with a different Middle-Eastern country, namely Iran. Germany is even working on a new international banking system that will bypass America in order to conduct business with terrorist regimes.