I don't think that's how you lose fat. You get rid of the exhaust generated during the chemical fat burning process. If you couldn't exhale you would still burn fat.
Out: CO2
That extra C atom comes from your metabolism. If you're in a calorie deficit, it has to come from your C atom reserve storage.
That's a way of saying that breathing faster won't burn more fat just because of the breathing: burning fat is a bit more elaborate than that.
Which is wrong, since breathing involves pumping air with your muscles.
Yes, and that will be your muscle mass as well as body fat if you're not exercising and maintaining a decent protein intake.