Madotsuki is the main character in Yume Nikki. Fans speculate that she is young, anywhere from nine to fourteen years old, although arguments can be made for any age. One notable argument is that she is "chibi" style and probably no younger than 16 if she lives alone.
Not much is known about this girl, and only what can be seen in-game can be considered canon.
She seems to be a hikikomori, or shut-in. This is supported by her refusal to leave her room- instead, she simply shakes her head. It is possible she is depressed, and the dreams are caused by her medication. (REM rebound, common for low dosages and withdrawal, or longer REM cycles.)
She lives seemingly alone in her room, doing nothing but sleeping her day away and occasionally going outside onto the porch.