1. Yes, obviously Japan housing prices have fallen from their insane 90s peak, but housing is still very expensive in Japan, and especially in urban areas where most Japanese (especially younger Japanese) live, space is famously at a premium.
2. I can barely count the number of times I've read articles on the reasons Japanese women don't want to get married. Unlike some Western nations, there is still a cultural expectation in Japan that women do a ton of housework and childrearing with little help from men, to the point that famously elaborate childrens' bento boxes are a source of stress. Many Japanese women with careers easily see marriage as a net negative, obviously different than decades past.
2. The reasons you listed are completely different from the one I responded to, and these are certainly potential factors. At least they’re often considered reasonable suspects in Japan.
Not "most" people live in where housing price is rising. Foreigners tend to see only metropolis. There are many people living non rural (some are urban? but having car is good) area but affordable housing price.