Since this is supposed to be a list of controversies about the Holocaust, I will answer you questions as such.
Why were the Jews targeted?
Short answer: Antisemitism
Long answer: Centuries of antisemitic propaganda particularly the notions that Jews were enemies of Christianity (refused to accept messiah, "Christ killers", etc.) and the writings of German theologian Martin Luther.
That opens up a big can of worms right there.
Brain worms?
Were the Jews killed under a Capitalist or Socialist regime?
Since we are talking about the Holocaust, they were killed by the fascist Nazi regime where the constructors of concentration camps and manufacturers of poison gasses were private companies -- capitalist. (This is not about the killing spree of the USSR.)
Why did Germany invade eastern Europe?
Not about the Holocaust specifically, though it proceeds it. To reclaim lands Hitler thought Germany had a natural right to (lands where Germans live or had lived), provide buffers, use of militarism to maintain control of the population, economic expansion, etc.
What did Germany plan to do with Eastern Europe after they conquered it?
Lebensraum. They planned to settle it with Germans.
Did the Germans plan to kill all Jews everywhere?
I don't know. The "final solution" plan was formed after the war started. There were lots of Jews well outside the reach of Germany's power, I don't know that Hitler was delusional or hateful enough to wage war to get every one of them.
Why didn't the Jews flee?
Many did, particularly before the war from Germany. Many were caught behind the lines once Germany began its war of conquest. Much of the world wasn't exactly welcoming to Jewish refugees, so where would they go?
Were the killings of German civilians justified when the allies didn't have to kill the same proportion of civilians when retaking France or Italy?
This has nothing to do with any "controversy" related to the Holocaust.
Is the punishment of the German people as a group for the Holocaust justifiable? Can this justification lead to another Holocaust?
What "group punishment"?
There are only so many times a teacher can tell students to repeat "Seven million Jews dies in the Holocaust" like a mantra.
I thought it was 6 million.
You haven't really delinated any "controversies" at all related to the Holocaust, let alone those that would be at a K-12 level. What's you deal?