Don Japanese fans write and create their own manga using characters and situations owned by other people?
Yup. We happen to be in luck because of the Japanese tradition of doujinshi, of tolerating and in some cases encouraging fan art and writings. They view it as good publicity. It’s still illegal according to US law and the Berne Convention, but nobody’s likely to make a fuss about it as long as it’s kept on a small scale. So, fan pages ahoy! Just don’t claim you own the copyright, because you don’t, and respect the copyright holders’ wishes.