"Terrain lower than your operative" means the terrain can't be below your operative (i.e., while it's on Vantage). The actual height of the terrain doesn't matter — even a small Heavy Terrain counts, as long as it's not at a lower elevation than your operative.
Shadow Passage is used when performing a Reposition, but the rule says "don't move it" — instead the operative is removed from the killzone and set back up. Since no movement through space actually occurs, the Wall terrain rule ("operatives cannot move over or through Wall terrain") doesn't apply. The operative can appear on the other side of a wall.
Although "Nowhere to Hide" says the operative "can move through parts of terrain features as if they weren't there," Gallowdark Wall terrain says "operatives cannot move over or through Wall terrain (this takes precedence over all other rules)." The Wall rule wins because it explicitly takes precedence. The operative must use doors and hatches like any other move.
When a Vespid operative uses FLY, it moves from point A to point B measuring only the horizontal distance. It can fly over terrain, Vantage points, and ceilings — obstacles in between are ignored entirely. Only the start and end positions matter.
On Close Quarters maps (Gallowdark, Tomb World), FLY cannot pass through walls, and cannot pass through open hatches.
FLY must be used for the entire move — you cannot FLY for part of the distance and move the rest. It is all or nothing.