This is very tricky. I personally would be interested to hear answers to your questions; I think each individual one is probably OK for MO (I think the diciest is probably "How did Soviet/Communist philosophy affect the choice of research directions that Soviet mathematicians undertook? Conversely, how did American/Capitalist philosophy affect the choice of research directions American mathematicians undertook?" in that any answer would be incredibly subjective.)
My advice is this: think about which aspect of this question interests you the most. Is it how the collapse of the Soviet Union affected Soviet mathematics? Is it how education and professional life differed between the Soviet Union and US (of course, one could talk more generally about the West and the Soviet bloc, but again, that's broadening things considerably)? Is it whether there are important lessons from the Soviet mathematics system that could be applied around the world today?
Whatever aspect it is, ask a question just about that one thing; probably it's best if you edit your old question and ask for it to be reopened (put a moderator flag on it). It might be you'll have to go through a cycle of editing and getting feedback, and editing more based on that. Then see how things go, whether you get good answers etc. Then over time, you can ask questions about the other things you were wondering about; probably knowing the answer to one will help you to shape other questions. You also might have some private discussions with the people who turn up to give answers. I wouldn't ask a bunch of questions at once. I think it's better to wait until one question has been answered, you've had some time to think about the responses, and people don't feel overwhelmed.