Your body burns energy at rest - the basal metabolic rate - and more on top depending on how much you move. This estimates both, then gives calorie targets for gaining or losing weight at various rates, and splits any target into protein, carbohydrate and fat.
BMR is what you would burn lying still all day keeping your organs running - typically 60 to 70% of the total. TDEE adds movement, exercise and the energy cost of digesting food. TDEE is the number to eat around; BMR is only the starting point for it.
Mifflin-St Jeor by default, which is the most accurate of the prediction equations for the general population. Harris-Benedict is offered for comparison and tends to read about 5% high. Katch-McArdle uses lean body mass instead of sex and age, and is better if you know your body fat percentage and are unusually lean or muscular.
For an individual, within roughly 10% either way. Metabolic rate varies between people of identical size, and the activity multipliers are coarse. Treat the figure as a starting point: eat at it for two or three weeks, track your weight, and adjust from what actually happens rather than from the formula.
Around 500 calories a day, which is roughly half a kilogram or a pound a week. Larger deficits lose more muscle alongside fat, are harder to sustain, and tend to end in rebound. Very low intakes should only be done under medical supervision.