19. (12 points) In a right triangular prism $ABC-A_1B_1C_1$, the lateral face $AA_1B_1B$ is a square, $AB = BC = 2$. $E, F$ are the midpoints of $AC$ and $CC_1$ respectively. $D$ is a point on edge $AB_1$. $BF \perp A_1B_1$.\\
(1) Prove that $BF \perp CE$;\\
(2) When $BD$ equals what value, is the sine of the dihedral angle between plane $BCC_1$ and plane $DFE$ minimized?\\
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