If I remember what it was like to be that age . . .and it wasn't too long ago. Then she definitely does care, but doesn't want you to think she does. Correction, she wants you to know how she feels about it without having to tell you and without having to talk about it. but she definitely cares about your reprimands and punishments. And, hard as it is to do otherwise, getting mad over her apparent apathy is not the best reaction. She sounds like she might benefit from a clean slate. I like the idea of setting down the house rules, and going over them with her, getting some input back form her as well. Although it might feel like pulling teeth, and she might claim to have no input, it is better to ask. At 16 she wants to feel like she has a say in some things and control over things.
Also, for someone who struggles with depression, and sugary breakfast is just asking for a midmorning crash. And teenage girls are also so conscious about their weight. If she claims to not have the time in the morning for breakfast, then I would provide her with two options for breakfast on the go, something like an apple or a banana, or a whole grain bagel. Protein is definitely key to keeping her energy level up, but it is difficult to work that into an 'on the go' breakfast without buying those ridiculous hot pockets or something like it. If she likes cream cheese, that, on half a bagel, is a great option for breakfast. Even the whole grain english muffins with some Nutella(tastes like Ferraro Rocher, and is made from hazelnuts and cocoa)provide hearty fiber and protein. That will carry her through the morning much better. Make it a house rule that you provide the basics for breakfast, but she is responsible for taking and eating her breakfast. I have a 14 year old and a 15 year old, but they are boys. At some point, you have to let them be responsible and suffer the consequences. It's 20 degrees out and I can tell them to wear their coats, but the hoodie looks 'cooler'(despite the claims that the coats don't fit in the locker) so they fore-go the coat and come home complaining of freezing their butts off. Does this mean that they will wear the coat next time, probably not, but they know there is a good reason why I am telling them to wear it, and when they have kids, they will go through the same thing with them. Some things, you just have to let go.
Work with her, listen to her. Although she probably isn't saying much, pay special attention to what she is saying. You are still the adult/parent but she is old enough to fall on her butt every now and then because you allowed her to make her own choices. Just don't say "I told you so" when it happens.
And even though it is unlikely, it is worth mentioning. Is she on any medication for her depression? If so, pay very close attention to her claims that she 'doesn't care' I have a younger sister who was on medication for anxiety and depression and claimed to not care about anything. Simplistically put, she ended up stealing from my mother repeatedly and getting involved with the wrong guy. She is off the medication now and can talk about how she was feeling at the time objectively, but is incredibly ashamed of her actions and states that, at the time, she really didn't care, she didn't feel anything but what she wanted that would make her happy for the moment. And she had no idea why she was doing what she was doing.
