I know somebody that does Open University part time and receives ESA (they're also in the support group). If the university can actually waiver your fee based on the fact that you are on benefits then I would imagine it may be allowed. That said, it might be worth asking the uni which benefits are considered eligible for the waiver (could be housing benefit as opposed to benefits for those out of work).
With regards personal statement, most postgrad programmes prefer people to justify their interest and ambitions for the programme. If personal resilience contributes to the course, eg something in healthcare, it may be worth mentioning, though for other courses it may be less relevant. There should always be an extra information section where you can explain that illness led to you getting a 2:2 though.