I'm not a History editor and rarely write in History, but based on how specific these categories seem, '1930s History' looks like mixed and specific quizzes about the '30s and 'USA in the 20th Century' looks like 100-years worth of mixed trivia based in the U.S. There is almost always a clearer fit, and in some categories there may seem like a bunch of options. If there are any issues, speaking to a category editor directly is a good bet. We can always move your quiz to the right spot if it's in the wrong one.
I'll leave your other question(s) to the History eds. Figured I'd give a bit of a general response as I face the same sorts of placement questions with people submitting in Entertainment (for example).