Answer
(a) Focus: $F(0,-2)$
Directrix: $y=2$
$Focal~diameter=8$
(b)
Work Step by Step
Equation of a parabola with vertical axis: $x^2=4py$
$y=-\frac{1}{8}x^2$
$x^2=-8y$
$4p=-8$
$p=-2$
Focus: $F(0,p)=F(0,-2)$
Directrix: $y=-p=2$
$Focal~diameter=|4p|=8$