Terri Penny's books are chronological and each book references past cases. Still Life, the first book, references the Arnot case but no others. At the end of Still Life, Gamache and Beauvoir are injured in the collapse of the stairs in the Hadley house. Gamache's leg is broken and Beauvoir has a head injury. Those are the injuries to which they refer in A Fatal Grace.
Richard Doesn't actually occur in any one book. The replay of it in Gamache's mind makes up one of the three plots in Bury Your Dead. The aftermath of that plays a role in all the books after this one.