I am not a teacher.
I would use "who."
"Affectionate" is a good word to describe a cat who likes to give and receive attention.
I think "petting" can cover any of the actions you describe, not just those where the palm of the hand is used. "Tickle" doesn't sound right to me.
"Fondle" is almost exclusively used for touching (usually unwanted) in a sexual way. I would avoid it. You rarely hear is used in a positive sense.