The default Arial font displays Japanese characters. However, if I try to use an imported font, I get the warning that dynamic fonts aren’t supported on this platform. Then the Japanese characters don’t display for that font.
What exactly is going on with this default Arial font? If dynamic fonts aren’t supported, then why does Arial work? Why can’t I get a different font to behave the same way as Arial?
You can use a Japanese font. Since dynamic fonts aren’t supported, the characters have to be pre-rendered to a texture. Since the maximum texture size is 2048x2048 (or 1024x1024 on older devices), that limits the size of the characters to fairly small dimensions.
As Eric5h5 mentioned, you can use Japanese characters, but you will be limited by the size of the texture that you import. The font that you downloaded is probably your best bet. The problem you probably encountered is that it “only” includes the two forms of writing (96 characters) plus all of the kanji (characters) that are taught in elementary school (about 1000), the characters used for city / prefecture names, and a few extra words for games like axe, armor and whatnot.
You may want to sit down with your translator and try to find alternative ways to write what you want or edit the texture to include the characters that you need.
Japanese support is trailing a bit, but with Unity coming out in Japan soon (if not already) I imagine things will pick up in the near future.