Foz
Let's deal with the second issue first.
Did you say that you have problems using the stairs? Did you expect to score for this?
DLA was based on a need for care whereas PIP uses very specific Descriptors describing a task that must be done, for example; washing your lower body, because of this you can only score for the activities that PIP actually looks at.
So, if an activity refers to a, b and c and your response to d, e and f then you will not score, in fact, you should not expect to score if you referred a, b and d.
As a Carer, you will be providing a minimum of 35 hours care a week, this may be physical support, emotional support or a combination of the two, many of the activities that you do for your caree will be similar to the PIP activities that you may well be saying that you have challenges in completing yourself.
As an example; perhaps your caree needs you to wash their lower legs and feet, if you were to say that you have problems doing this for yourself as well then the DM will see this as a conflict as they would expect the physical task of washing your caree's feet as being very similar to that of washing your own and yet you are saying that you can do one and not the other.
You need to explain how you provide care to the person that you do and yet are still so limited yourself that you qualify for PIP.
As to your ESA, I can't say without more information about the type of ESA you receive, your living arrangements and what benefits any persons you live with receive.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
