Okay - I'm in abit of a rush so forgive me if I haven't gotten the full gist of things (I skim-read).
As somebody with an eating disorder, debilitating anxiety, paralysing depression, and a pending ADHD diagnosis (though none of this means that I am a professional or that I know exactly what you are going through by any means), it seems to me like you are setting yourself up for alcoholism and an eating disorder. I am sorry if that sounds harsh, but believe when I say, eating disorders are so easy to fall into and so tough to escape from. My eating disorder started at least 5 years ago, maybe longer. I was in denial the first two years and used justifications just like you have above. Eventually, it evolved into a raging, uncontrollable monster.
My relationships, studies, mental health, physical health, finances, and mood have been torn to shreds, and I'm still trying and failing at picking up the pieces. The biggest thing I discovered though, was that my ED is really a coping mechanism - something to hide behind - a way of coping with deeper issues (i.e the depression/anxiety/ADHD/stress etc.)
The part about cancer - I think (and I may be wrong) that you are suffering from either OCD, or some other type of condition that causes intrusive thoughts. I think you should see someone about this. That time it was cancer, but who knows what the next one will be? And who knows how it'll affect your life/actions?
The ED always helps initially, it helps to distract from other things. But eventually it will catch up to you, and you will be worse off than when you started. You said you are more anxious but studying better. Again - this is not sustainable in the long run - you will burn out and end up worse off.
Let me give an example - I was very much in the same position last year - unmotivated, isolating myself, not wanting to get out of bed etc. I started to take on ALOT - I'd be out from 8am until 11-12 at night. All day I'd be out, occupied, moving, doing things. For a while, it really helped. I was more excited, motivated, social. I was distracted from how I felt on the inside. I was always going, going, going, never taking a rest, never stopping. And it lasted a while - it was good. My mind felt clearer. But eventually, it all caught up to me. I burned out like I never have before. For 3 months, I isolated myself, alone in my bedroom, not speaking to anyone. not going out, doing nothing. I couldn't sit my end of year exams, because I was just (mentally) paralysed - literally my mind would just not work anymore. I was fried. I now have to repeat the year.
I'm sorry for any repetition or poor articulation, I'm in a rush. Obvs my situation is not your situation. But for me, I was so focused on education, grades, this priority, that priority, that my mental and physical health slipped more, my ED intensified, and in the process, I lost the things I was so focused on (education etc.). I'm still not better - I stress from the moment I wake up till the moment I sleep. I'm literally getting stomach pain and nausea from stress. I've stopped caring about anything and have lost interest in everything - friends, studies, sports, hobbies - everything. I'm not okay. And from reading what you've said, it seems like you aren't either. I have refused to prioritise my MH for so long, that now I'm forced to unless I want to lose ANOTHER year.