If she gives her place of residence as the hospital, I would imagine that is because she was living there, probably in a nurses home. i.e - her place of residence.
I dont know, but I would think it is unlikely that there are any records of her training anywhere. You could try checking out the London Metropolitan Archives website to see if thgey hold anything, but if they do, it is highly unlikely they will be accessible online.
Have you found Isabella in 1911 census, to see where she was then, and what 'rank' within nursing she was at then?