Are the 4" radius zones for dominating infinitely tall on this mission? Or do they extend outwards from the centerpoint like a hemisphere?
It's not explicitly stated anywhere, but as a general rule circular Zones in Infinity are cylindrical straight up, while circular weapon templates are spherical. So since you're talking about a ZO, I'd go with straight up/infinitely tall.
Compare to: http://infinitythewiki.com/en/Zone_of_Control Troopers have an awareness of their surroundings thanks to rear sensors or plain (or augmented) hearing. A trooper's Zone of Control is an area 8 inches extending from the border of its base, as measured vertically or horizontally. The Zone of Control is projected upwards and downwards in a cylinder 8 inches high. Circular Templates are as layed. Only the blast focus extends for Smoke Grenades upwards but always in the limits of that cylinder. For Transmission Matrix I would keep it similar to the ZoC ruling.
Is that 8" up and 8" down? As that is what the first sentence says, however that makes a cylinder that is 16" high from top to bottom.
That is how Zone of Control works, yes, however that is an entirely separate concept. I don't really see them as related. I would look at this as more similar to a terrain/visibility zone, since it is tied to scenery/objectives, not a trooper.
