I've had the same sort of thing (though not including the illness) from my step-daughter. She's very, very wilful and stubborn. It came very close to breaking up our relationship more than once, even having me staying in a hotel. Fortunately, she departed to university, and we only see her occasionally now. Life is bliss!
Having to look after herself has drastically changed her outlook and behaviour. When she's with us, she now does at least a bit of tidying and cleaning etc, and does things we ask her to. She also respects us and our home a lot more. So, ghastly teenagers do change, but it will take a lot more than you yourself can do to make it happen.
Some suggestions: when she was in the trash-the-entire-house mode, we fitted locks on internal doors. "If you can't treat the house with respect, you won't be using it unless we're here". This one really used to get to her. Tidying up: her room we just left a festering mess, anything of hers elsewhere in the house, we asked her to move it, failing that we just threw it into her room. Though, I have to say, after a few years her room was a health hazard - but, she had to live in it, not us. Encouragingly (for us) she was so ashamed of her room, she wouldn't let her friends see it. Food: we tried to buy more food we liked and she didn't, so that her choice and amounts she could eat (while we were out) were limited. Washing: she had to bring down what she wanted washing, we never got dirty stuff out of her room for her. Bath: we usually left it dirty after we'd used it.
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