Hello Brawburd - our cat does the same! When she suddenly lies down in front you, she just knows that whatever you are doing, you will stop for a second to stroke/tickle her. If I am really busy and don't do it, I always feel guilty and have to give her an extra bit of attention later!
Well I've got 8 of the little furry tripper-uppers, and they all do this sort of stuff.
I think that the lying down in front of you thing is something to do with submission...giving you their tum to tickle shows they trust you. I don't have stairs, but walking around here is a real furry minefield...there's always 1 of them in the way...maybe they just like being trodden on...
Bathroom I reckon is because they know that for at least a few minutes you are going be a sitting target for them to perform their cutest attention seeking antics & will probably get a bit of fuss!
The only worrying thing is that one of my cats after following me into/watching me in the bathroom now uses the toilet regularly. Makes you wonder what goes on in their heads. Its also quite off putting when you know your alone & someone starts using the toilet!