YES on the anxiety. I'm hesitant to say 100% improvement, but closer to 90%. I think that there are two kinds of anxiety --- anxiety around certain emotional triggers and anxiety that your body spontaneously throws out when it's struggling to digest certain foods. I had the latter, but I haven't met too many people who've experienced that kind of anxiety. Sometimes it felt like anxiety without rhyme or reason, other times I would have uncomfortable abdominal pain concurrently with the anxiety and could feel the connection. Are the burping and anxiety ever coordinated?
The way I finally got rid of this anxiety left me with a paleo lifestyle, but that was more coincidental. My doctor, and other doctors that subscribe to functional medicine methodology, has had a lot of success treating anxiety and depression using an IgG Food Allergy panel blood test. The Ultramind Solution by Mark Hyman discusses how delayed food allergies can cause anxiety for upto 3 days post eating an allergen. In my case, I had allergies to soy, gluten, and dairy, which led to a more paleo lifestyle. But I also have food allergies to citrus fruits, blueberries, coffee, carrots, cabbage, and broccoli -- none of which paleo would demand me to give up.
Getting rid of the allergy foods was a huge lifestyle change in itself and led to a 90% reduction in depression and a 50% reduction in anxiety. I was able to kill off the rest of the anxiety by abstaining from sugar, including fruit, and regulating my sleep schedule. Paleo doesn't call for abstaining from fruit, but that's just something I needed to do.
So my point is, paleo could help with your anxiety, but it might not be enough.