Visible crew/equipment: Near the beginning when the Phantom is rescuing the little boy from the back of the truck, as he is hanging from the rope bridge, the safety carabiner holding him up is visible several times.
Visible crew/equipment: After the villain's have been in the cave at the beginning of the movie (one gets killed by a "skeleton") and they run out, the Phantom is chasing them on his horse. He grabs a bad guy by the shirt and throws him into a tree. Watch when the guy hits the tree- it moves, indicating it's made of foam or rubber for the stunt guy to hit safely.
Answer: She was preoccupied trying to escape from the bad guys and annoyed that a guy in a purple suit, was trying to save her, when she said, "I can do it myself." It was most likely later, in New York, when the met face to face. Kit and Diana, when she put two and two together. Again was too preoccupied trying to save the world to pause and confront him.