Why does my mom believe in fairies and have a downturned mouth?

No way to know. I would be concerned if, and only if, your mother shows other signs of severe mental illness -- fairies influencing her, stealing her thoughts, persecuting her, making her their queen, etc. Don't try to understand people's folk / cultural / cult beliefs. Some medicines given to people with known mental illness cause abnormal mouth movements; perhaps unknown to you, she is being treated.