1. The workouts can be increased by a bit each time
2. the principal or specificity states that if one area is trained, that specific area improves. Flexibility is a good example of specifically going for being more flexible
Fasting and starvation tactics are bad because they are essentially depriving your body of what it needs to grow. So your body is basically digesting its self to run its basic needs. It digests fats, but at the same time it also starts to digest muscle and other tissues.
A laxative diet is the ingesting of minerals or chemicals that help you defecate (such as magnesium) which can be harmful in several ways. They can prevent your body from properly absorbing all of the nutrients in the food that you are eating and can disguise other issues such as diarrhea, which in some cases can be a symptom of something serious. (And also has the potential of giving you a hernia or irritations.)
Liquid diets are diets that consist of liquids. which are often times missing a large chunk of basic necessities of your body, from some missing fiber or iron. To some just being plain ignorant. There are a very few that actually have everything you need to grow and survive.
I'm actually in online school at the moment and I've also been behind quite a bit, my best advice is try to get in contact with the teachers, I don't know if your online school has a center where you can go in and get help but mine does and if you just tell them what you are going through I'm sure that they can help. Worse case scenario you wanted to take a few days off from school and you'll have to lie about being sick or something and they will understand. I hope I helped.