Sorry to hear that. Her score looks decent, so I'm guessing it was an income issue or thin, short file.
Did they give her the reason for the decline?
If she wants to try for the Student Amex does she need to reapply or can she ask to be considered for the student card in her reconsideration letter or by phone?
All of the inquiries are recent.
No, they won't use the same INQ. They'll pull a new one if it's not the same day.
Other AmEx people, would they use the same inq to apply for a different product? Alternatively, would the inq be de-duped?