You're not supposed to have artificial sweeteners or milk during CM's. Half and half or heavy cream in your coffee is fine, so long as there is no sugar or AS's added to it.
In the old CAD, they allowed artificial sweeteners, but later research found out that they triggered the hunger hormone just like regular sugar. Some folks do drink Diet Coke or have AS in iced coffees and such, but it is a case of YMMV, and the Heller's no longer recommend using them during CM's. Also, you might want to get a copy of CALP- the veggies list has also changed from the original CAD.
Good luck! The plan really does work, but I find it extremely hard trying to do it with a family to feed. If it was just myself and my husband, it would be easier, lol. Also, lot of cooking involved, just like all low carb diets. Nothing quick and easy to buy on the fly for CM's, unless you get a roasted chicken from the deli and a salad, which isn't always fresh.