I find that cats can be very interesting creatures. I own one myself , and have been very observant of its habits. They enjoy the comfort of their master by rubbing on the bottom of your legs as well as what would call unintentional petting. That means they would see your hand laid over the couch or down at your side and would rub their hand in your head, regardless of whether you wanted to pet them or not. Some of them see you as more of their parent than their master. This explains the need for the kneading of the paws on something soft that you love, like your favorite sweater or blanket, and wanting to get under the blanket in bed just to be close to you.
The other thing that I have notice is the clutter issue. If you do not cleanup piles of dirty clothes, or have old boxes and paper laying around, you may find cat droppings on them. They can see this as their litter box if it is not cleaned out, or can't get access to it. They will also do this if they are upset with you or someone in the house, sucjh as another cat. Another factor is they may not like the litter. The cat that I have will tip his cat pan over and will leave his droppings elsewhere if there is hard pebble litter in his cat pan. Thank God, that there are a variety of litters as cat are like people, there is preferences involved.
The third observation is the way that they sleep. You should view it as a compliment when a cat sleeps on its back or very close to you. That means they fill safe with you, and will hide behind you if they fill threatened in anyway. If your child is chasing them, they will even come and get under the blanket with you while your are asleep to seek protection. Cats are also known for trying to hold a conversation with you. They will sit right next to you just start meowing . If you meow, or simply talk back in english they will respond. They think they are human anyway. The longer you engage them, they will keep meowing, as they figure you are understanding what they are trying to say. Don't be surprised if they respond on action to something you said, outiside of the ordinary sit and stay commands. I told my cat once to go in the bedroom and be quiet, and he did just that. You have to realize they feel like part of the family and sometimes one of the kids. One time my children were acting silly over a toy, and I demand very strongly for them to go to their room, my cat lowered his head and ears and went with them.
I can honestly say that cats very curious creatures, but also very comforting and fun to have around. Cat lovers everywhere I know share this same sentiment. From being very easy to please and handle, to also being very frisky everynow and then, cats are incredible pets.