At age 5 it is normal not to nap anymore. If she is not eating, maybe she doesn't like the meal you have given to her, she might be one of those picky eaters. Or, her not eating could be her way of feeling a sense of contol. She should not be going outside without permission though.

What kind of "structure" do you have taking place for her? Does she go to kindergarden or nursery school? How about looking into a dance class for her? What do you do together with her? Take her to a zoo, a local museum? Look in your local town paper too and see what kind of things you can do together, little fairs, perhaps take her to a local stable to ride a pony.

I understand that children need to follow rules, but I also think it would be better if you bonded better with her, and that can mean taking her places and doing things together that will be "fun" for her.