Can a person only nominate themselves? Can community members nominate other community members?
You can only nominate yourself. If you think someone else would be a good moderator, the most you can do is to encourage them to nominate themselves.
You can only self-nominate. As noted on the recent election page:
NOTE: The only way to be nominated is by nominating yourself. The way you do that is by clicking the "Nominate yourself as a Candidate" link below and then answering the questionnaire on Meta.