Which is correct people’s life or people’s lives?
Simply put: a life is SINGULAR and lives is PLURAL. Don’t confuse with: She lives in London with People’s lives are at risk by taking this vaccine. People’s life is INCORRECT at all times.
Is it each other’s life or lives?
It all depends on the number of entities involved. If two entities, “each other’s life.” (There is only one “other life.”) If three or more,”each others’ lives.” (Here think of the missing understood words, “of the” between “each” and “other.”