Looking at their clothes, I'm sure they have been on the run for a while. I was expecting that her parents were trapped in the Gate like Sung Il Hwan. Now that we know how beat up of a parents they are, no wonder she was named "Karen"
She can't eat anything except human meat! This is Tokyo Ghoul inspired! Also she can drink coffee. This is less worse than TG because she can taste food but can't swallow