There will probably be a few different answers on this one. The best one is to ask your doctor, but since you asked I'll give you my opinion: Coke Zero, as well as all other "zero", "light", and "diet" products are sweetened with artificial sweeteners like aspartame and sucralose. Though these sweeteners are approved by the FDA, there is evidence to suggest that they are actually worse for you than real sugar because of the chemicals they contain. Some even go so far as to say that they can be carcinogenic. Personally, I won't eat or drink anything that has those products in it. If I wanted a Coke, I'd drink a regular one even though it has caffeine in it. Depending on how much you drink, a small amount of caffeine each day is considered safe for baby while you're pregnant.
Of course this is just my two cents. Others may have different opinions. Your best bet is to ask your doctor. If that's not possible, lots of states and organizations have hotlines you can call to speak to a nurse or other expert and get their opinion. Where I live, the number is 811, but its probably different everywhere. If all else fails, I'd do a bunch of research online, and only trust reputable sites.View Thread
I'm not a doctor, but I'm fairly familiar with the paleo diet. I can't see why it would harm you or your baby as long as you are getting enough calories, vitamins and nutrients. The paleo diet is full of healthy foods and I can't see any doctor not supporting you in that as long as its done properly.View Thread