Which are all the hints that lead to Cordelia's solving the mystery in An Unsuitable Job for a Woman?

Cordelia is suspicious about the circumstances of Mark’s supposed suicide. Her examination of the photographs reveals how it might have been staged. When she gets to know his friends the Tillings, their overly friendly behavior to her, being lower in class status that they are, raises her suspicions.
Cordelia is pointed toward the truth about Mark’s identity through an inscription in the prayer book, which had belonged to his deceased mother, and information from Mrs. Pilbeam about his overseas birth. Conversing with Dr. Gladwin, the mother’s former physician, along with genetic evidence, directs her toward Mark’s father—Sir Ronald Callender, the person who hired her—once she learns that Mark was adopted. Not only was she right that he was the killer (with a financial motivation), but her suspicions that the suicide itself was staged and that the scene had been tampered with are confirmed: Mark’s real mother, very much alive, steps forward, admits she did the tampering so that the murderer would be unmasked, and kills Sir Ronald.
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