I hate the idea of "cheat" meals and days. It's just food, as long as you don't go over your calories you won't gain, even if you only eat junk for a few months. It also (imo) implies that one is on a diet, which tends to end (like 30 day diets), instead a person should try to form healthy habits.
One "cheat" meal or day won't undo any progress just like a day of dieting won't make you lose.
But I've also heard it helps people who tend to binge often.
MFP is great but it tends to calculate calories a bit wrong (in my case too low, while I'm trying to maintain) For weightloss I calculate my tdee (https://tdeecalculator.net
) and the just subtract 500cals from it. (and make sure I don't go under my bmr)
TLDR: Yes you can lose weight by not working out (but exercise is good for you), yes you can have cheat days even if they go over your calorie limit. Just make sure you're eating enough.