Pretty much every mountainous region in the mainland of Japan, except for Chiba prefecture, has bears. Most people do not live in the mountains, which is why bear sightings tend to be limited to the areas with (a) significant human population, (b) proximity to mountains.

They do. My parents live in a mountain village in Japan and never step outside without bear spray and a bear bell. There have been some grim local stories — bears taking pet dogs out of yards. For people up there, it's a daily fear, not an abstraction.

Weapons in general are far more highly regulated in Japan, and of course the citizens don't have the right to bear arms.