What's wrong with her skin? Anything a course of twenty quid antibiotics would cure?
She might be hyperthyroid if she's got thin, it's really common in elderly cats - it costs £30 a month for medication but my old girl has doubled in size (and is peeing in the right place now) since starting 4 months ago.
Yes they would, if they felt that she was ailing to the point that her quality of life was not good. But if her quality of life would be ok and it is just a matter of not being able to afford the treatment then ask them about getting her treated and repaying gradually. Or if you are recieving benefits/tax credits the PDSA might treat her for free.
If you have a cat you really need to save a little money to cover vet treatments. I know that's hard but it's our responsibility as pet owners. But do check out to see if the PDSA is available to you if you can't.