Our little cat, 2 years old, keeps washing people's hands. It is a recent thing but a bit freaky, everyone someone sits down she is up next to them, the reach to stroke her, get a little gentle nip (to taste?!) and the she washes them to the wrist if allowed.
She is spayed (4 months ago) is a bit thin (has been wormed, flee'd, jabbed etc) and is eating and drinking well. I am still concerned it is her kidneys, she certainly doesn't like her sides being stroked.
My cat licks & nibbles me if she's feeling particularly affectionate, or of she's busy grooming herself she might do me while she's at it . She sometimes is especially enthusiastic if she tastes/smells something on me (fake tan bizarrely is her favourite, I discourage her from licking it!) maybe she's tasting people's skin? I think cats like to lick the salt from sweat as well(could be making that up). If she's nipping them gently maybe she's just being friendly?