Exercise calories

I'd say eat them back, or at least half of it. If you lose weight, awesome!
If you don't, stop eating them back. If you lose weight, awesome!
If you don't, go back and ensure that you are accurately measuring your caloirc intake, you're probably underestimating calories at that point.

Ahh, the age-old question. Eat the calories, or not? And, if not, let them accumulate over time for a big reward of something hedonistic? Personally, I tend to leave the exercise-related calories alone, but if I have an exceptionally productive day, I might use some of them for a rare treat (like, say, ice cream).

Without a body fat number BMR is a rough estimate and I wouldn't worry too much about it. It simply allows you to calculate a starting neat or tdee.

For tdee method you should include exercise in the calculation and not eat them back, but I think that another fine way to do it is what you are doing. 2 lbs a week is a safe rate of loss when you have plenty to lose, so do 1 lb by cutting calories and then exercise on top of that. So long as you feel good, the exercise isn't suffering, and you don't start losing way more than you should, stick with it.

If you don't lose as expected, it could be that the estimates don't fit you perfectly and you can adjust.

I'm wondering if you told mfp 1 lb, though, as I actually think it would give you more calories for that.

It seemed strange to eat back my exercise calories.
NO WAY! Eat back exercise calories?
Folks, do this any way you want, but I love eating back those calories. That's part of my motivation to train like I do.
SHHH....

The deficit that it shows is only a subtraction of the calories you consume from the calories it shows being burned for normal daily activities. I thought it meant that was the deficit you were suppose to have. It really doesn't mean anything. The more calories you eat the less the deficit will be. Subtract your calorie intake from the number it gives for calories burned from daily activity. That's all it is.