Exercise calories?

MFP is build around the concept that you should eat back the exercise calories.

You will find people adhering strictly to the mindset that YES you should always do it and you will find people adhering to NO you should never do it....and a broad spectra of everything in between.

I would recommend trying to eat back your calories and find out what works optimally for YOU - personally I try o eat back most of my exercise calories, but more often than not I can only eat back about half of them. This works for me - but it may work differently for you.

yes, the program is designed that way. There is already a deficit built into your goal so if you burn more you need to eat it to keep the deficit where it is and not make it TOO large which can hinder more than help.

Provided you know a fairly accurate burn from an HRM or other device. If you use MFPs burn estimates then only eat half of it to be safe because they overestimate. Most cardio machines at gyms overestimate too.
You want to eat them so your body has fuel, but not if the number was entered way too high, in which case you'll eat up your deficit and just maintain instead of lose.

So eat, but be conservative with burn numbers.

I do not eat them back as when I eat I feel like I am only maintaining my weight. So for now I decided to eat 1/3 or half of them. Everyone is different so I think you should observe your body and decide accordingly.