hahaha. my cats act like dogs too. they roll over to get you to pet their tummies. and they meow when they want something like my dogs. its very funny.
i hate cats. get an alligator.
All of my cats except one don't really care about strangers. The cable guy came over one day and while he was standing at the door talking to my mom, one of my cats jumped on him. x.x They seem to like really tall people. xD;;
I think your cat is suffering from "Duuurp" syndrome. It's a disease where cats do everything that dogs do, except that they look stupid.

He's deaf obviously.
And I've known a few cats that run into doors, they're not retarded.
I had a cat (Crookshanks) who thought he was a dog, I swear. Me dog Sadie likes cats more than dogsoO.o
Maybe your cat just has a quirky personality ? Like people, I suppose animals can all be different in their own ways as well.
Your cat sounds a lot like my cat Boo. I read several places (and was told by our vet) that generally white cats with blue eyes are born deaf, or go deaf later in life.
Boo never startles at any loud noises, or even so much looks our way when someone calls her name or anything like that. I don't think she's completely stupid though, just stubborn because she somehow always seems to notice whenever the catnip container is being shaken lD;
And I know a lot of cats that don't wake up/look when people walk by. Your cat probably already knows your smell by now, and realizes that you being around her doesn't mean danger, so she feels safe enough to sleep comfortably around you and your family.
My friend's cat has a disability. It doesn't walk, it wobbles. Falls over sometimes... :c Her family saved it from being put down, because of it's disability.
My cat's just a brat.
Oh. And today my brother saw her sitting at the top of the steps, like a human, with her legs crossed and her front paws resting on her legs. O_O He knocked on my door to show me, but once I opened to door she came running towards my room. Haha. I wished I could've seen it. I've seen our dog sit like a human before, but never our cat.
Animals can have disabilities too. I had a cat that was deaf. She didn't come when we called her, wasn't afraid of sudden loud noises (crashbangboom xD), tv, etc. We thought she was a bit weird at first, but after some research, our family learned that she was born deaf because she was entirely white with blue eyes. don't try to argue with me on that one, it's genetic. :P
[edit] oh, forgot a big one. she meowed REALLY loud, that gave it away too. and she developed diabetes near the end of her life... we had to give her insulin shots twice a day which was very sad, but we tried to take care of her and her disabilities the best we could. she was a very nice cat though. :)
My cat does things like that. Hell, even the vet told us she was dumb!