I don't know if it's a myth or not; I think I read about the body recovery in the second edition of the book Titanic: Triumph and Tragedy and the book Titanic: An Illustrated History. It appeared crushed and had soot on it. They could only identify him by the belongings in his pockets.That Astor was crushed by the falling 1st funnel is only a myth. His recovered body actually did not show any sights of it.
Why in the staircase, because the film skript had it so.
So he most likely just drowned or froze to death then? If he died in the staircase like in the film, his body might've been ejected from the ship because the staircase broke free from the ship.
I've always found it odd that Astor did not give all the money he had in his pockets to Madeline, as he knew he would not be needing it any longer.