Ask an Property Solicitor. Get an Answer ASAP.
No it will not hurt your nomination and also please be aware that the council cannot discriminate. Of course, each scenario is dealt with on a means led basis (financial situation) and on its own personal merit (so in this case, your disability and health will prevail).
Please also remember the council have a duty to prioritise those who are in need especially during the current pandemic. I would begin with the application as soon as possible and fingers crossed you can get located in Cornwall as you require. I have located their website and all the information you require can be found here -https://www.cornwallhousing.org.uk/find-a-home/
I hope this helps and please do leave positive feedback. If I can assist with anything else, please do let me know.
So yes, as you are on medical benefits the council cannot and will not refuse you - if anything, this will make you a priority on their list.
No, so as you are in medical benefits they will already have record of this.
I am really sorry to hear of your ill health - I really do hope your situation gets better over time. I do advise to proceed with your application to the Cornwall council as soon as possible. They will note your current situation re ill health and will prioritise you as you wish.