I read somewhere that "timeout" should not exceed the age, because time to a child is totally different than time is to us. Based on that and since she is 5 years old, the timeout should be no longer than 5 minutes. Set a timer and sit with her until the time is up.

As far as going outside without asking goes, you may need to install locks on the windows and doors that she cannot tamper with and/or open without an adult present ... I know she's five, but she doesn't understand the danger or consequences of going out alone and unattended, and to punish her for that is inappropriate, because it is the adults responsibility, not the childs.

I would ask her what she would like to eat, fix it for her (regardless of whether you feel it's nutritious or not - sometimes empty calories are better than no calories at all), and once she earns your trust with whatever it is - even if it's chocolate cake and orange juice - then she'll probably come around to more nutritious offerings later on. If she says she's not hungry, don't push her or force her to eat because that can very well set her up for disordered eating later on in life.

Remember there's an extra layer of issues you are dealing with here, so above all be as patient, gentle & kind as you can with the wounded child ... And, if you feel that it is too much for you to handle, then call and employee all the professional help and opinions to help y'all through it as you can!