Park between Barons Court and West Kensington, with free on-street parking. Get the tube one or two stops to Earls Court, change at Earls Court, then two stops southbound to Fulham Broadway. Unless it's a Wimbledon District Line train, in which case no need to change at Earls Court.
What makes it worse is the theory test is only valid for two years and then needs re-taking. I think the driving instructors can block book tests, maybe that is the best way to do it? At least it would then be in the right town.
https://www.gov.uk/book-pupil-driving-test
Have had season tickets at Gillingham, Withdean and the Amex. Though I never felt that Gillingham was a season ticket, more of a loyalty scheme with a promise of a seat at Withdean.
I have heard that you get more allergies from male cats than female cats, not sure why. With the nosebleeds, if they are consistently from the same place you could ask for them to cauterise your nose, a five minute job.
Do you have a spare room in your house that she could stay in? This is what we did with both grandparents and great-grandfather. It means they get to spend their final years with their family, rather than alone with strangers.