Not sure about Alec (haven't paid enough attention to videos pre Hugh, I'm too young and, frankly, dislike bassists with egos if they refuse to play more than 4 strings) - but richie has always just used a normal mic stand as far as I'm aware. Generally speaking in a rock setup you get two kinds of mic stand - one which is straight and easy to use as a prop but doesn't allow for much space for an instrument behind it (such as Jon's) and one with a boom (the arm that extends at an angle) that allows more space for an instrument (such as Richie's).

I don't know the story of the mic stand, but speaking as a very atheist singer even I could be considered something of superstitious. Whenever I play I wear the same jewelery, go through the same tired rituals and, yes, generally speaking, use the same mic stand. I trust it - if you use one that belongs to the house you risk a loose screw and spending the entire night holding it up, or they'll give you one with a boom that you can't move around with. Granted I'm not as bad as a friend of mine who had hers custom made, side-lights n all but it's a common theme.