???
No, it's just a way of showing that they're the ones in control. It's kind of like on Family Guy when Peter shoves Meg's face into his butt then farts.
No, it means they want to jump you and have sex with you if you are willing.
Well, yes, they 'trust' you in the sense they are saying, "I'm the boss here, so you can kiss my rear end!"....;-D..
I know right? My cat does that too!
Nah. it is purely practical. Your face is soft and warm, nicer to sit on than a rough carpet or the cold floor.