BMR, TDEE, Calorie confusion

The never eat below your BMR thing is a myth. You can safely ignore that.

Now, as for the rest, I think your confusion stems from the fact that you're attempting to combine two different approaches: TDEE versus MFP.

You have two choices:

1) Use MFP. Plug in an absolute weight loss goal (I'd recommend no more than 1lb/week with your stats -- that's a 500-calorie/day deficit) and set your activity level to sedentary. That should give you just under 1400 calories as your net goal. Then, you log your exercise on top of that, and "eat back" your exercise calories -- either all of them, or, since MFP often overestimates workout calories, you can try eating back only a percentage. So on exercise days, you'll be eating more than 1400 calories, but on non-exercise days you'll be eating less. The pro to this method is that it adjusts itself based on the actual exercise you do, not based on the exercise you *think* you'll do. It's good for people who have a hard time sticking to a workout plan or who are sporadic with their exercise. It's also fairly easy to set up with MFP.

2) Use TDEE. Custom-set your goals in MFP to 1724 calories, which should be a pace of around 0.8 to 1 lb/week. Then, *don't* log your exercise and don't eat back any additional calories. Aim to stick to that 1724 calorie goal regardless of whether it's a workout day or not. The benefit here is that you don't have to mess around with logging and calculating exercise calories, and it's easier to meal plan when you have a relatively consistent calorie goal. But you have to make sure you stick to your workout plan; if you stop or slack off, you need to have the motivation to eat less, since MFP won't be keeping you accountable.

Some people find one method works for them; some find another works. Try them both out and see what works for you.

And most importantly: Remember that no online calculator is ever going to be exactly accurate for your body. They use formulas and algorithms that can help you approximate. But your actual TDEE may be higher or lower than what the calculators say; the only way to find out is by tracking what you eat and what you lose in the real world. If you lose weight slower than anticipated, adjust your calories downward or your exercise upward. If you lose faster than anticipated, do the reverse.

Oh, and don't forget to recalculate every 5-10lbs of weight loss, since when you're smaller, you don't burn as many calories just by lugging your own weight around, so you'll have to adjust your TDEE downwards.

Hope this helps!

You are comparing two different methods of accounting for exercise and then two different methods of subtracting a deficit (percentage versus 500 cals per lb of weight loss a week). But the numbers are very similar.
TDEE is 1881 with no exercise, minus 20% = 1505
MFP with no exercise, minus your projected weight loss goal = 1400

Comparison with exercise would be:
TDEE = 2155 with exercise 3 days a week (exercise 3-5 times a week for 30-60 minutes)
Take off 20% = 1725
MFP = 1400 base calories but you would log and eat back exercise calories.

Either method works so choose the one that suits you best, if exercise per week isn't consistent then MFP is probably better.

As a personal trainer I was taught that you should be NEVER eat less than BMR. This also lowers your BMR and messes with your brain because your brain needs those calories to be able to function. If you do your body goes into starvation mode and your body will hold on to everything you eat and turn it into fat. This is the reason why most people plateau when they do fad diets because they're body goes into starvation mode. Then most people get discouraged and quit eating healthy and they end up gaining all the weight they lost back. Plus some extra because they messed up their metabolism and lowered their BMR

Eating too little does not cause your body to turn everything to fat. That has been debunked. I urge you to read some recent reputable medical research on this topic! If that happened, POWs and such would be obese, not skeletal. ditto ppl with anorexia. Yes, you can slow down your system *some* if you undereat drastically for a long time. But from there to making you fat, it just is not true.