A
There is no legal requirement for your to claim JSA, however, you will not receive any other benefit payments at this time, so claiming may be a matter of necessity! If you do make a claim for JSA then you should not present a Fit Note initially as this will likely lead to your claim being rejected, once your claim has been accepted then you can present one and be excused any Job Search requirement for up to 13 weeks.
As far as I am aware Hardship Payments can only be made if you have an active ESA claim, which you currently do not.
As an alternative and dependant on your personal circumstances, your husband can make a claim for Income Support as a Carer.
As this is an Administrative MR and not concerned with entitlement, it should be handled quicker, but there is no required timescale for an MR, of any type to be completed within.
You do need to be aware that even if your MR is successful, it will not remove the requirement for you to attend an assessment, this is a decision made by the Assessment Provider and the DWP are very unlikely to interfere. Given you have gone through this process once already. I think it unlikely that they will now.
My best advice is for you to involve your MP again, this time with Maximus.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems