How many calories does an hour of boxing burn?

I mean like just punching a bag, getting tired, resting for a few secs, punching for a few secs, etc.

Also, how many calories does 20 minutes of light walking burn? For example...walking to class in the mornings.

Thats too general of a question for most people to answer, it depends on your energy output, intensity, weight and so many other variables it would be nearly impossible to get an answer to it. But you can size it up to a similar cardio exercise (running, biking) and maybe get the calorie counter off a treadmill if you feel like you are working equally as hard you have an approximate calorie count. Of course when the treadmill stops it doesnt mean the calories stop burning, your body continues burn fat for up to 2 hours after a high intensity workout, which is why you should avoid eating during that time.

can i drink a protein shake during that time?

Well the reason for not eating during the immediate time after you do your cardio is so that you burn stored fat calories rather than food or calories you put into your stomach. Drinking a protein shake may interfere with this but it will also prevent muscle from being metabolized so it really depends on your goals. Do you want to lose only fat or just cut weight in general? Try supplementing with heavy doses of glutamine while cutting and drinking your protein shake about 45 minutes after cardio but immediately after weight training.

Doing cardio on an empty stomach is not recommended as the body will use both fat and muscle storages for energy. You can eat whatever you want (healthy foods are recommended though) WHENEVER you want, as long as you keep your caloric intake/output ratio of that day at a deficit. Just watch your calories, eat plenty proteins that fill you up with whole grain carbs and good fats and you should be fine.

I really shouldn't be giving you advice since you're a colts fan, but whatever.

It depends if you are trying to simply cut weight or cut weight and maintain muscle. Some people are only interested in losing the weight, in which case glycogen levels arent necessarily as important, meaning youd lose the weight fast running on stored calories and keeping ur post cardio meal a good mix of protein and carbs up to an hour after working out.