It is a cat's instinct to mark their humans with their scent; claiming us as their territory. Some mistake this act of "marking" as a sign of affection. When they rub against you with the back of their head and the rest of their body, he just wants other animals to know that you are "his".
But when they bump you with the front part of their head, a cat behaviour called "bunting", that is when they are truly showing affection. He might rub along your chin and nose, just like how he'd rub around his mother's head for nursing. Some cats even drool when they get too carried away.
An insecure cat might shy away when we reach for their head. In this case, the chest will be more respectful and enjoyable for them. When a cat stares at us, they want our attention, and a semi-closed eye represents trust. They are saying: "I don't have to worry because I trust this person".
Wondering why your cat comes face to face with you and starts sniffing? This is another sign showing you that they care. Cats greet each other by going real close and sniffing around – it's their way of saying "How are you today?".
Cats that roll onto their backs and stretches out in front of you (with their belly area exposed) are saying, "I'm happy and secure." In general, dogs and cats feel vulnerable when their bellies are exposed so take it as a compliment that they are comfortable showing you their bellies!