The Codex said "Saved", but one of my characters was missing afterwards. Do I have to fill in the short key?

No, from version 1.9.24. The short key next to a character's name (for example "john") is now optional: leave it empty and it is made from the character's first name when you save. A character card that still cannot be saved is named in a message and stays on screen with your typing, so you can fix it, instead of disappearing while the Codex says "Saved". In an older version, give every character a key before pressing Save.