Rotating a Segment About a Point on a Line

As shown in Figure 1, the line $y=kx-8k$ intersects the $x$-axis at a point $A$ and intersects the positive $y$-axis at a point $B$, and the area of $\triangle AOB$ is $32$, where $O$ is the origin.

1. Find the equation of line $AB$. 2. As shown in Figure 2, $P$ is a point on segment $OA$. Rotating segment $PB$ about $B$ clockwise by $90^\circ$ produces segment $CB$; segment $PC$ is then drawn. Let $m$ be the $x$-coordinate of $P$, and let $S$ be the area of quadrilateral $PABC$. Express $S$ as a function of $m$. 3. Under the conditions of part 2, as shown in Figure 3, the extension of $BC$ meets the $x$-axis at a point $E$, and $D$ is a point on the extension of $EB$ beyond $B$ such that $\angle ADB=4\angle CPE$. If $AD+BD=BE$, find the coordinates of $D$.