Hi! I know this response is quite delayed, so hopefully you have since found some answers. :-)
Because CMT only affects the nerves, but affects so many of them, there have been found to be countless different symptoms, even across family members.
Vertigo is not necessarily a symptom, however loss of sensory perception in the feet can lead to limited proprioception (which tells you where you are in space ... so that you can keep yourself from falling over!). The main ways to have good balance exist in your inner ear, your sensory perception, and your eyes. I have CMT 1A and have poor balance in my inner ear and am gradually losing most feeling in the bottom of my feet. So, to keep my balance, I have to use my eyes!
While it is not supposed as common, CMT can potentially cause spasms in the back and stomach muscles, as well as the peripheral muscles in the legs and arms. I would question whether it could cause the face spasms, but it might be possible. I have had back spasms before, but I mostly attribute them to muscle 'tiredness' from compensating and using my back muscles when everything else is too weak (ie my arms).
More studies are being done to see how pain affects memory. It is thought that severe pain (ie short-lived extreme pain) can negatively affect memory, in both long-term and short. I myself am currently experiencing memory loss. I am only 22, but I was diagnosed with CMT at 8, and have already undergone 4 foot surgeries (so I am near the extreme end of the spectrum). From my perspective, chronic pain can easily be equated to severe pain, as it becomes harder for the body to endure the longer it exists. Your brain has to function in a certain way to process pain, so the more it needs to process the more 'space' it takes up from potentially having 'energy' remaining to store or access memories. I would recommend looking into different forms of pain treatment ... whatever seems to work best for you. Aside from that, there should be no reason that CMT affects memory, as the brain is comprised from a different 'type' of nerve, which is built using a different portion of the DNA sequence than the one(s) affected to create CMT.
In regards to heat intolerance, I have noticed in recent months that I am regularly overheating when I should not be. I am not certain if this is related to CMT, but my Physical Therapist did note that MS is known to have similar temperature problems. As that portion is also due to nerve issues, I would consider it to be a plausible explanation. I find putting a cold rice pack (dry rice inside of a sealed fabric bag that was in the freezer) on my neck, back or head to be quite helpful. I have had temperature issues with water (not having any idea if it is hot, cold or in-between, and changing on a regular basis) for over 5 years now, and I am certain that is directly related to CMT. For the dizziness, I would recommend paying attention to your blood sugar. I doubt that it is related to CMT, other than potentially through the 'tiredness' of the brain. I have had similar symptoms, but have always attributed the change to hypoglycemia. (And I have actually fainted a few times)
Good luck in your endeavors and learning to understand the workings of your CMT body!
-Jessica