No.
This is definitely not normal for anyone to not eat and think your body is going to be okay with that. Your body needs nourishment to use as fuel to keep yourself going and growing.
If you are doing this as opposed to dieting in a smart way, you need to re-think your strategy. This will backfire on you.
Basically in order to get rid of that fat you have to give your body a reason to use it as energy for an active metabolism. The mistake that most people make is not eating anything in order to lose this fat.
You're not sleeping because you're not eating. Your body sensing food deprivation, so it stays awake until you find food.
no you need eat and get sleep.
Not eating means dieting and no sleep means worrying about not losing weight. What a futile exercise?