Answer:
The first answer: Yes, they do move in the books as well. Since, the movies depict almost exactly what the book says, then it is a sure thing that the stairs moved in the book as well.
For instance, in the Chapter 'The Potions Master', it says;
"There were a hundred and forty-two staircases at Hogwarts: wide, sweeping ones; narrow, rickety ones; some that led somewhere different on a Friday; some with a vanishing step halfway up that you had to remember to jump. Then there were doors that wouldn't open unless you asked politely, or tickled them in exactly the right place, and doors that weren't really doors at all, but solid walls just pretending. It was also very hard to remember where anything was because it all seemed to move around a lot. The people in the portraits kept going to visit each other, and Harry was sure the coats of armour could walk."
Hope this helped! :)
Me adding on to this: This is how they find the sorcers stone's hiding spot.
Explanation:
