Breastfeeding Calorie Count?

Depends. I would think 500 is too much. Maybe try 300 and see how it goes. When I was breastfeeding, the weight just melted off. After weaning, it crept back on unfortunately.

I believe breastfeeding is in the food section if you search it...gives you back 500. Depends how old your child is. But I would not eat less then that if Bub is little.

Adding it as a food "does" add back 500 calories but it may not add back any macros depending on which entry you pick, and if you pick one it may not add back calories in your macro percentages if you have something other than the MFP default of 65% carbs 15% protein 20% fat.
Adding it as an exercise would at least add the extra calories and add them across your macros as any other "cardio exercise" does
Both food and exercise routes of adding it require you to add it every day.

My home > goals > change goals > custom
increasing your daily calories "forces" it to be across your macros, and has another advantage of being set it and forget it unless and until you lose 10lbs and get prompted to update your fitness goals / profile.

I'm not BF, but I am pregnant. I manually increased my calories, so I would be sure to eat enough. I'll up them again in probably a month. For me, it's just easier to change my caloric needs, as opposed to logging it as fitness. In the end, it's the same, except this way, I know I have those carbs, proteins, and fats to distribute.