Okay, so apparently, BMR is how much calories your body burns while at rest. And a pound of fat is about 3500 calories.
So if I have a BMR of about 1300 (used BMR instead of TDEE just to be safe), can I lose exactly a pound of fat if I fast for 3 days, while having a couple of cardio exercises just to ensure I burn fat, and not muscle?
Yes, but only after you are in full ketosis. If you are an experienced faster, that could be as low as 72 hours, but if you are a beginner it could take 2-3 days. The only way of knowing for sure is measuring blood glucose/ketones.