When designing an overflow$-$type spillway with a design flood rate of $800$ m$3/$s$,$ when the elevation of the apex of the spillway is $108$ m and the planned flood level is $112$ m$,$

$(1)$ Find the width of the spillway,

$(2)$ Find the road surface curve using the WES method. Assume that the slopes of the upstream and downstream sides of the spillway are vertical:horizontal of $3$:$2$ and $2$:$1,$ respectively, and the flow coefficient is $2\mathrm{.}0.$ And ignore the access head to spillway.

$(3)$ Determine the point where the downstream slope $(2$:$1)$ begins.