Diet sodas do not count towards your water intake. What counts is simply water (mineral water, spring water, tap water, etc).
I did not say you were eating too many cups of vegetables. You are eating too many from the "Other Vegetables" list if you are having 1 cup of spinach and some broccoli in the same day. So you should be eating less of these and more from the "Salad Vegetables" list. The total has to be 3 cups every day during Induction.
Chewing gum, if sugar-free, is sweetened with sugar alcohols. If you don't get diarrhea from consuming them, then it means that your body is metabolizing most of the sugar alcohols. Thus, you should be counting them towards your net carbs.
You are over the sweetener limit (three servings), btw. Two cans of diet soda and five pieces of chewing gum add up to more than three servings of sweetener.
Something else I forgot to mention about vegetables. Most of your net carbs should come from them, but this cannot happen if you are having about 10 g net carbs from the chewing gum, 2 g from cheese, another 1-2 g from eggs.
My advice would be to ditch the chewing gum, diet sodas and Jell-O cups, and instead eat real, nutritious food. Not only will your figure benefit from this, but also your health.