Yes they do, well white hairs. My, once jet black cat, first turned more brown and then little white hairs began to sprout out around the whisker area. Now she has loads of white hairs it's really sweet. She is now 17.
I know, she sleeps a lot but give her a cardboard box and she becomes a kitten again.
Not much, dogs do more. My dog is 12 years old and she used to be all black but now she's grey round her muzzle, eyes and feet.
Dogs do, not sure on cats.