Suze
As far as I am aware once you only receive NI Credits for JSA, there is no requirement for you to Job Search or attend the JC+, even if you could receive NI Credits with ESA, which I am not sure you could, they are exactly the same as the JSA ones, so there is no advantage that I am aware of.
As to the MR, the DWP recently extend there guide times for MRs from 2 weeks to 4 weeks, clearly they need to go a little further.
Gordon