Are there any basic employment opportunities in the Stack Exchange community?
I'm not entirely sure what you are asking about. There are no paid positions specific to the Japanese Stack Exchange. All of the admins are volunteer community members.
The Stack Exchange network has a job-finding site https://stackoverflow.com/jobs, but it's mostly developer focused. I vaguely recall the Stack corporation itself hiring Japanese speakers as part of the rollout of the Japanese programming site: https://ja.stackoverflow.com/, but that was several years ago.