What is normal rate of fat loss? Is it changing depending on how much person has left to normal BMI (considering he/she doesn't want any extra muscle weight).
There is not a "normal" rate because of so many factors including stress, amounts of sleep, age, metabolism, gender, etc. However, as a good rule of thumb, I've found that aggressive fat loss for men can typically be 1 - 2 percent of their body weight and for women 0.5 - 1.5 percent. That means at 300 pounds, losing 3 - 6 pounds per week for males and at 200 pounds, losing 1 - 3 pounds per week for females is possible.
Typically I've found people can lose more weight than that per week, but when it's faster than those guidelines, the extra weight is often water weight and muscle. Water weight is an illusion - it really isn't helping you with your goals, so when you first switch to a low carb diet for example and lose 8 pounds in a week, you've really only burned a few pounds of fat and then flushed water from your muscles. Muscle weight or what we call "lean mass" also isn't good to lose because that will slow your metabolism and actually make it harder to burn fat.