nicholson
There is no required timescale for the assessment phase, at the moment waiting times are at least 10-12 weeks.
You don't need to use a SAR, you can just contact the DWP office dealing with your claim and ask for the PA4 if you have a F2F or the PA3 if you don't, at that stage I would not expect there to be any other documents. If you do use a SAR then again send it to the office dealing with your claim.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
