A few thoughts.
First, I lived with cats from when I was seven, to seventeen; and then, on-and-off, as an adult...I have watched their behavior, and thought about it. Which, really, is the function of cats. They're not pets, like a dog is a pet - a cat is animated furniture; it's living art; it's a study of life. Like an ant farm, only housebroken (one hopes).
The purring. Our huge tabby more-or-less adopted me (you don't own a cat, a cat may choose to own you) and would sleep on my feet night (a high-metabolism teenager, I slept with bare feet poking out).
Purring is not "contentment" as the women who write cat-care books tell you. Sick and dying cats purr. Also, cats are inherently dangerous, and instinctively territorial.
Purring is a signal to other cats - and anyone who understands cats - that they're open to company and socialization. Male cats have territories and also neutral territories where they meet females, or otherwise socialize. A purr is to tell other cats, the guard is down, I'm not going to maul you.
A cat who wants something, like breakfast, will purr.
The behavior the one cat offered, kneading with the claws out, is "milk-treadling." Kittens do that to, essentially, milk the mother's breast. It's been said that a domesticated indoor cat is basically a kitten, arrested development. Probably true. If a cat milk-treadles you, it either wants food or wants the comfort of a mother's belly.