Tribunals can only consider your circumstances around the date of the decision to stop your benefit. Any improvement or worsening of health since then cannot be considered. Therefore you have to describe your health at that point in time and any medical evidence should relate to near the date of decision.
You've said (on page 3) it can be all said in the past tense at an oral tribunal in six months time but in my DLA letter on the date of the decision in September it says "If your care or mobility needs have changed, you must tell us immediately. Your award can be looked at again and a new decision made, if needed. Your money may stay the same, go up or go down."
If your circumstances change, you should inform the DWP and they may make a fresh decision. But that would be a new decision and not relate to your appeal hearing, which relates to the decision in September.
I would not expect your ESA to be affected until it is due for review.
