1. As the author suggests, a lot of that weight loss is just water. It'll come straight back again.
2. Getting into ketosis can take more than a day. Hell your body might even still be processing the carbs for quite a while as your food makes its way slowly around your digestive system.
3. 7 liters of water is tonnes. You risk flushing out your minerals. It's really not recommended. Adding some salt isn't enough.
4. Zero calories vs low calories when doing a low-carb diet doesn't really make a difference, your limitation is just around how much body fat your body can convert to useful energy when you need it.
5. When your body runs out of body fat it can easily source, it starts eating muscle. That's not just your arms and legs, that's things like your heart.
6. If you're not eating your body tries to convert whatever it can get into food. That would include the multi-vitamins he takes.
7. When you come out of ketosis, you should do it slowly. Transition from a high fat, low carb, small protein to increasingly more carbs and proteins. Grabbing a take-out or ribs and ice cream defeats the point.
8. Fasting only really works over short periods. When your body realizes something is wrong your survival mechanisms kick in, you go into starvation mode. Your metabolism drops and you start conserving energy rather than burning it.
To lose 1kg, all this guy has to do is make one small adjustment to his daily routine. One less sugar in his coffee, one less take-out a month, a little more cardio, etc.