temporary self-employment and ESA

Hi everyone,
I am attempting to claim ESA following a hip fracture due to recently diagnosed osteoporosis (increased risk of further fracture).
I just received my 'customer statement' having had my initial call cut off( by them) and they didn't ring back. When I rang back,the claim was taken up by another operative but the statement I just received was still largely gobbledegook and full of absurd errors.
After speaking to three different operatives today (in order to register the errors) I was promised that 'although they weren't able to help' that I would be telephoned on '3-hour ringback'. Five O' Clock came and went -with no call.

Anyhow - if my initial,basic claim proves to be this complex - I am very worried about what to do about the exam board work (on a self-employed basis) that I have done for about a decade.
I moderate GCE coursework - it only lasts for 3 weeks in January and May/June -and I have an NI exemption certificate due to the short period of work and not earning enough to pay income tax.
As I cannot walk and am not allowed to attempt it for some time - the only reason I can still agree to do this work is because I can do all the work at home and online whilst still in my bed! The work involves reading and checking that the candidate has been given fair marks for their work. My carer can open the parcels for me and make the necessary trips to the Post Office.
Do you think that mentioning this would make the system blow a gasket - or do any of you undertake similar work whilst on ESA?

I would think you'd have to ask for permission to do 'permitted work', but if it did not fall into these guidelines then it may invalidate your claim and you'd have to reclaim ESA after it had finished? Only my gut reaction - the mods will know more than me...