How many eggs should a inactive teenager on diet eat a day/week at the max?

Depends. Eggs can be part of a healthy diet, in moderation, some fat in diet increases satiety. Many good diets out there all with pros and cons. Good balance of fruits, veggies, lean protiens and whole grains, avoid "simple sugars" such as candy and soda and "white starches". Many on a low carb diet see improvement in there harmful cholesterol and lipids profile. Mindfulness and moderation go a long way.
None is too many. Being a happy and healthy vegan, I feel that the best approach is no eggs. Afterall, you are trying to drop your weight, so why sabotage your efforts with such a high calorie food such as eggs? Instead, you will feel plenty satisfied by sticking to an unprocessed fruit and vegetable, and whole rice and wheat grain diet, without added sodas, added caffeine beverages, mild, cheese. Eggs = +++fat!