1. The majority of the time, your fat leaves via respiration as carbon dioxide. Fat has 3 types of atoms- carbon, hydrogen and oxygen. The carbon has to come out as carbon dioxide, the hydrogen has to come out as water and at last the oxygen is partitioned between the carbon dioxide and the water. In other words, you breathe it out and the rest disappears as water: tears, sweat and urine! Although that is the case, by only breathing more will not help you losing fat, theoretically you would lose some fat, but not going to be enough to show on a scale. Not unless if you are workout more. (information obtained from a study by Professor Brown at the University of New South Wales)
2. Why is preserving muscle mass important? Scientists use the weight of muscle to estimate resting metabolic rate (RMR), which is the number of Calories a person burns at rest. More muscle equals to a higher RMR, for instance if we’ve got two males who are same size and weight, but one with greater lean muscle mass and one with greater fat free mass, the person who has a greater lean muscle mass literally would burn twice as much than the person who has a greater fat free mass at rest. However try not to mix up RMR with TDEE (Total Daily Energy Expenditure) which takes activity into consideration.
Therefore as an EXTREMELY general rule, if you exercise regularly, consume a balanced diet and the reading on the scale is the same or even higher, don’t smash the scale and be all disappointed, you probably did a small amount of good towards increasing your lean muscle mass as well as metabolic rate, besides, Keeping fit, staying lean are a lifelong journey, keep up the good work!