<image>As shown in the figure, in the rectangular coordinate system, points \( A \) and \( C \) are on the \( x \)-axis and \( y \)-axis respectively. \( CB \parallel OA \), \( CB=8 \), \( OC=8 \), \( OA=16 \). 
(1) Directly write down the coordinates of points \( A \), \( B \), and \( C \) and the area of quadrilateral \( OABC \).
(2) The moving point \( P \) starts from the origin \( O \) and moves towards \( A \). It stops when the line \( PC \) divides the quadrilateral \( OABC \) into two parts of equal area. Find the coordinates of point \( P \).
(3) Under the condition of (2), is there a point \( Q \) on the \( y \)-axis such that the area of triangle \( CPQ \) is equal to the area of quadrilateral \( OABC \)? If such a point exists, find the coordinates of point \( Q \); if not, please explain why.