Do we eat more calories if we exercise!

You should eat 1600 calories today. Or at least 1400 (half the exercise calories)

That is the way the tool is designed as exercise activity is not included in your activity level. If you're eating 1200 and burn off 400, you're only leaving your body 800 calories to work with...to make your heart pump, your lungs work, etc...and that doesn't even include daily general operations.

The more active you are, the higher your calorie requirements are...1200 is already a huge deficit from maintenance...I'd wager you told MFP you wanted 2 Lbs per week...1200 is the floor so it won't go any lower than that, but basically it's estimating your non exercise maintenance calories to be, let's say 1,800 calories per day (as an example)...you could play with the app and figure it out more accurately.

So if we do the math, you have a 1,800 - 1,200 = 600 calorie deficit. Now you exercise...let's say 400 calories...you could eat those calories back (provided they are accurate) and till maintain a 600 calorie deficit...so you could eat 1,200 + 600 = 1,600 and still maintain a 600 calorie deficit because with the additional activity your maintenance would have moved to 1,800 + 400 = 2,200 and 2,200 - 1,600 = 600 calorie deficit still.

To be safe, I only use about half my calories burned. I find that if I eat all I've burned, I gain a pound or two. Weird!