You aren't obliged to help or like your friends' friends. How many of us can honestly put our hands up and say we like all of them? You are looking for every excuse under the sun not to give this woman her marching papers but it's not going to solve this problem. This woman is not a good flatmate and if the rental situation was different, she'd be better suited to living on her own. Maybe that's why she comes to life when you're in bed - it gives her the chance to live as if she has the place to herself. Your relationship with her sounds like that of a primary school teacher repeatedly telling their class to be quiet. It works for a while but the noise always starts back up again.
If your mutual friend was saddled with a flatmate like this, do you think they would tolerate it for long?
If your friend doesn't know what this friend is like to live with, then she'll understand, and probably apologise for asking you to let her move in.
If she does know, and didn't tell you, well then she's not much of a friend
She's more trouble than she's worth. If you want a peaceful night in your home then do the sensible thing and ask her to leave.
You don't owe her anything. Yes probably tough having an eating issue but the sheer lack of awareness for anyone else is inexcusable.
I have a sleep disorder and used to have an ED too. So I do eat later than other folks. However, I would never disturb anyone by cooking that late. She can put a microwave in her room or get a mini fridge. You shouldn't have to be kept awake.