My words literally betray me.
A player controls a hexagon if the relative majority
of miniatures in that hexagon belongs to that player
(example: the blue player has 2 miniatures inside the
Central Hexagon, while there is one Ghost and the
red player has one miniature: the blue player controls
the hexagon and gains 4 Victory Points).
Rules give a 2-1-1 example here. Also the rules include ghosts in the talk which should imply they should be counted. And the use of the word "miniatures" rather than player miniatures should also indicate that ghosts count. In practice, all the ghosts are generally killed already in my experience.
The answers are:
#1: Nobody Controls.
#2: Green Controls.