Juliana.Rivers wrote: ... Are they positively correlated?
Is TDEE a better measure than BMR of how we should monitor eating and calorie intake
What should BMR be on fast days compared to Non Fast days
Not correlated, but additive.
BMR is the minimum energy level that your body requires just to keep you alive.
TDEE includes BMR. Lying in bed, flat on your back, breathing and doing nothing else is BMR. Simply reaching up to scratch your nose, adds to the calorie clock of your day's activities - your TDEE.
Think of it as being forced to leave your car's engine idling all night long. (Let's say that the starter is bad so if you turned if off, you couldn't restart it.)
In the morning you've burned a certain amount of fuel from all that idling, right? That represents the car's BMR. Now if you drove somewhere, your car's TDEE is the total of the fuel burned idling (all night) plus that consumed to get you to your destination.
The car's idling kept it alive and potentially useful, just as your BMR does for you. So the only choice you really have is whether you want lie in bed breathing (idling) or get up and do something (drive someplace).
HTH