While I know you think "both" is the right answer to all of them: 1, 2, 3, 7 and 9 are the USSR, 6 and 8 apply to both, the rest describes the Nazis.

1. Equating the Holocaust and the gulag system is not just idiotic but outright malicious. The Holocaust was not "a network of forced labor camps". The Nazis had extermination camps. Many also died on the trains to the death camps. They also massacred people directly. The goal of WW2 was to depopulate Eastern Europe and establish "living space" much like the Westward expansion of the early US.

2. The Nazis believed that Jews were migratory parasites lacking any allegiance to a state, draining the host country for resources before moving on to the next country. It equated this with "international bankers" who likewise had no loyalties. The anti-capitalism was rooted in antisemitism, not the other way around. The talk about bankers was what we would now call a dogwhistle.

3. The DAP (later NSDAP) was the only nationalist party that tried to appeal to the working class because it represented the largest voting block. Their politics were however always defined by ethno-nationalism ("völkisch" nationalism to be precise) and antisemitism. The other nationalist parties generally favored a return to the monarchy.

4. That describes most military conflicts in history. However Germany did not want to capture Eastern Europe, it wanted to depopulate it. While the Western Front was largely about revanchism, the Eastern Front was entirely about creating "living space". The Soviet Union did engage in imperalism (although Lenin would disagree based on semantics he invented) but it was more interested in creating distinct Soviet republics and most of its territorial expansion happened in WW2.

5. While the USSR was not what I would call a functioning democracy (and even less so than the USA), even Stalin did not have the same level of power as Hitler. The Bolsheviks embraced bureaucracy and strongly believed in the rule by committees. Given the internal power plays within the party, it's fair to describe Stalin as dictatorial in practice though. However the cult of personality around him was mostly built up after the fact and against his wishes and didn't transfer to his successors like in the DPRK.

6. So was the US? We think of these two as examples of massive propaganda because they were created when mass media became available and we have an outside perspective on their propaganda. The Nazis were however way ahead of the Soviets during their time and the US didn't go to quite the same lengths even before the end of the Cold War.

7. The DAP was explicitly anti-Marxist and embraced what Marxists call "class collaborationism" (as opposed to Marxist class struggle): the idea that despite the divisions, all Germans belong to one people ("Volk", defined by "blood and soil") and differences must be set aside to protect this. When the DAP was renamed, the "socialist" was deliberately chosen to appeal to the working class but the party strongly considered alternative labels to distance itself from Marxism. Any actual anti-capitalist tendencies that survived the Great Depression were eliminated during the Night of the Long Knives when a few holdouts like Strasser were killed to align the party closer with Hitler's vision. The Nazi government also generally did not "nationalise" businesses (not more than other capitalist countries at least), it disowned Jewish people and those deemed enemies of the state. Often these businesses were then sold for very low prices to existing companies. During the war, some companies were also offered cheap access to slave labor in order to aid the war effort. The famous Autobahn and other "accomplishments" of the Nazis were built by companies. I've actually heard people jokingly credit the Nazis for making the idea of "public-private partnerships" popular.

8. If you have to put it so vaguely, you might as well apply that to many other countries including the modern US. I don't think this is a useful framing even if I think that some of the things you're lumping into this both countries did worse than others.

9. Again, you're describing authoritarianism and trying to turn this into a gotcha. Arguably the Nazis had controlled their media less than the Soviets because they would just literally kill or imprison people whereas the Soviets had to create mock trials and torture them until they provided plausible confessions.

I won't even address the rest of your post because it's completely unrelated to your claim. Remember: your claim is that the NSDAP was a left-wing socialist organization and that by implication the Nazi government was socialist and therefore left-wing. You have provided no evidence of that. At best you've demonstrated that the USSR was similarly authoritarian and in many ways did not adhere to its supposedly socialist ideology in practice. That is the opposite of what you claimed to intend to demonstrate.