NZtechfreak: I will say this "repair mode" talk smacks of pseudoscience and sets off my BS-ometer. On the fasting days the body will be in a catabolic state in which it consumes its own tissues to meet metabolic demands, and unfortunately the predominant tissue consumed in this state is protein as the body does not have stores of protein in the way it does fat and glucose (protein is contained primarily in muscle, which is not a storage tissue in the sense that the others I mentioned are). It may be this "repair mode" is a dumbed-down way of attempting to make some actual science accessible to laypeople, so I will look into it further (if for no other reason that I will need to discuss the diet with patients who enquire). None of this is to say that the diet doesn't work or is a bad idea per se, only to note that this rationale seems weak (the diet in essence looks to condense the usual daily hypocaloric intake recommended for weight loss into two days, achieving on average the same kind of calorie intake on over the course of a week, certainly I can see how this has adherence benefits). If I were to do this I would be taking care to ensure I was eating adequate high-quality protein amongst those 5-600 calories.
I'll have a read through the book and see if I can put proper language behind it. The idea is when there's plenty of energy the body creates new cells, when there's less it repairs existing ones. The TV show did all kinds of measurements of bloodwork, you may understand more of it than others.
I don't do weight exercises on fast days, as I want to minimise muscle loss. You can take supplements, I've read BCAAs are a good option - can't remember what it stands for, but it's amino acids. I do weight exercises on eating days.
It may just be pure calorie restriction that makes you lose weight, but it makes it easy to restrict calories. Moderate cardio exercise while fasted really does seem to help.