Milk, water are best. The first rule is to eat healthy foods. The second is to avoid foods that can cause harm. Carbonated diet beverages add no nutrient value, replace liquids from healthful drinks, and damage the teeth according to dentists. Avoiding them in pregnancy and if breastfeeding might help women and their families avoid them later also.
Hydrate and HYDRATE! Hydration is very important in pregnancy and one of the best things to drink is skim milk. Plenty of water is also good. But diet drinks are ok too if you don't like the taste of plain water. Flavored water and mix-up drinks like crystal lite are ok. Carbonated diet drinks would be down the list because of the carbonation, but they're still better than the full-sugar versions.
Yes. You can but do it in moderation. You are better off drinking water.
Yes. Water is probably the best diet drink you can drink during pregnancy. Soft drinks, whether diet or not, are usually not the best drinks in pregnancy. I would suggest healthier drinks, such as juices, milk, electrolyte drinks such as gatorade or powerade rather than purely synthetic drinks. I would stay away from energy drinks.