Here's a thread from a while ago - I've got a post in the middle of it that explains my experiences.
http://www.salongeek.com/nail-geek/86686-manicures-elderly-care-homes.html
As for charging, speak to the home and see what rates would be in line with what the clients can afford. Keep your rates reasonable but fair, but give a good, thorough service - a lot of residents have little physical contact and they like massage and a kind, warm hand.
Don't write off homes for the "very very old" - these ladies like to feel and look good too! There are so many levels of care - speak to the site managers and see what they say about whether or not their clients would be receptive. And keep in mind not everyone in a home is elderly - I have several clients in their early 40's that live in residential care, and they want their regular manicures and waxing.
The homes themselves might pay for your police check, so see if they require that (my homes offered to pay for me).
I hope you find a good fit! Best of luck!