How many calories would you lose if you only ate 500 calories in a week?

You will lose weight, depending on your weight. A person weighing more than you, will burn more than you. When you say burning 500 kcal you mean in exercise? Because you'll burn more in a day, around 1500-2000 kcal a day. You certainly don't want to hang on to those concerns you may get, so I will not give you a bunch of lectures. Still, I'd wish you would notice that your metabolism will slow down. Soon there'll be harder to lose weight.

Well, weight loss depends on kcal in and kcal out. One kilo of fat is like 7000 kcal. If you'll say that in a day you burn 2000 kcal, while consuming 500, you'll be having an advantage of 1500 kcal a day. That means 10500 kcal a week, and over a kilo is gone. In the theory this is the correct weight loss, though it won't sound sensible when a person loses 1 kg by eating 1600 kcal a day and burn around what you do. But of course it really depends on weight.