Does a promoted piece have to go on the square the pawn has moved on or can I promote by turning my rook upside down on its existing square
The FIDE Laws of Chess are explicit:
184.108.40.206 When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’.
So, the answer to
Does a promoted piece have to go on the square the pawn has moved on
can I promote by turning my rook upside down on its existing square
And if you turn your rook upside down then, as far as the rules of chess are concerned, it remains a rook.