The humans place a control token in an adjacent unoccupied region when the airfield is activated. Can they then build another airfield and continue to expand if they have enough build points and adjacent unoccupied regions? Or continue to build anything they want there for that matter?
No, you cannot do that. You can only build in a region you controlled at the beginning of the action.
Also, crystals in regions with Trog tokens are still counted when someone activates scoring, correct?
Only if someone controls the region.