The given equation is $x^2=-16y$
Here, the coefficient of $y$ is negative.
Hence the parabola opens downwards.
On comparing this equation with $x^2=-4ay$ 
$-4a=-16$
$\Rightarrow a=4$
$\therefore$ Coordinates of the focus $=(0,-a)=(0,-4)$
Axis of the parabola is the $y$-axis i.e $x=0$
Equation of directrix  $y=a$ i.e., $y=4$
Length of latus rectum $=4a=16$