Does TDEE include BMR calories or is it on top of them?
It includes it. TDEE is BMR multiplied by the activity factor, so the resting expenditure is already folded into the final number; there is no need to add BMR again on top of TDEE.
Why does the TDEE calculator show a range instead of a single fixed number?
Because TDEE is the product of two estimates, BMR and the activity factor, and both carry their own imprecision. The 10% range below and above the central value exists so the tool does not present a single number as if it were an exact measurement.
Which activity factor should I pick if I only exercise twice a week?
That usually falls between "lightly active" (1.375 factor, light exercise 1 to 3 days a week) and "sedentary" (1.2 factor, little to no exercise), depending on intensity and the rest of your daily routine. Since the gap between adjacent categories already weighs hundreds of calories, it is worth picking the more conservative one when in doubt.
Is TDEE the amount of calories I should eat?
TDEE is an expenditure estimate, not a diet prescription. It is a reference number for understanding maintenance, surplus or deficit; any decision about how much to eat, in any health context, belongs with professional guidance, not this calculation alone.