First question answered,you can switch between 's' mode,'d' mode and manual mode whilst moving.You needn't be stationary.
Second question answered,the same thing has happened to me,if you don't put the hand brake on when on a hill before putting it into 'p' or the car slips back before putting it into 'p' the gearing seems to get stuck.This can be worrying because you have to force the gear stick out of 'p' and it can go with one hell of a clunk.You just learn once it has happened once or twice to apply the hand brake before putting into'p.
I hope I have explained it enough.