This one is on the tip of my tongue. It's a manga that I read online somewhere between 5-10 years ago. The main character is a high-school-age boy who comes home to find his father dead, I think either drained of life (leaving him skeletal) or with his head bashed in. There's also a girl with very long black hair. It transpires that she's a demon, albeit probably not the one who killed his father. I want to say that his father was a bit of a deadbeat, prone to gambling debts, so the boy was already used to being pretty self-sufficient. Also, the dad winds up possessing something, maybe a small animal, and therefore is still around, giving bad advice. Anyhow, the demon girl can turn her hair into various shapes, including using it as a weapon, and using it to form wings to fly. She's ignorant of a lot of aspects of human society, which means we get a lot of cute misunderstandings. I'm not certain if she's mute, but I think she talks very little.
I remember there being one episode where the boy is playing sports with his classmates in summertime, and the demon girl keeps showing up with hot drinks, hot snacks, etc, with mention being made that when it's hot, it's traditional among the Japanese to drink and eat hot things because it makes the body sweat more, which helps cool you. It turns out that she was trying to get a hot bath working at the house, so all of the snacks were her trying to use up all of the excess hot water. Another episode involved a self-mummified monk found in a temple who is brought back to life somehow. I think there was also a bumbling angel who opposed the demon girl. And there was a demon who very unconvincingly tried to disguise himself with a trenchcoat and a hat who deferred to the demon girl. I think that the series ended with the demon girl revealing her true nature, that she was the Devil herself, ruler of Hell, but that she wanted to stay with the boy. And I think he learned that she was responsible for the death of his father, but he forgave her for it.
Now that I mention that she was the Devil, I want to say she was named Lucy (as in Lucifer). I think the comic itself was entirely black-and-white, maybe with some shading, but little to no color.