greeneyes
I'm afraid you need to be persistent on the Helplines, calling as soon as they open may help.
No, I would not expect them to confirm that they have updated your mobile number.
I'm afraid I can't give you an address for the DWP as the one that you need to use will depend on what Benefit Centre your ESA and PIP are being managed out of, be aware, they may be different.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems