Hi Jonte
How much weight assessors put on relative's letters it is difficult to tell, but if you have them available we would always tell you to include them.
We can't give you any timescale for how long you will have to wait for an assessment. It could be as little as eight weeks or it could be much longer.
Regarding your ESA you will need to contact them and ask. Some people receive that sort of statement when they have an occupational pension suddenly being paid.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems