A suggestion for the "Disease, Death, and ..." category would be Flu by Gina Kolata (published in 1999). It's about the 1918 influenza pandemic and efforts over the years to isolate the virus and discover why that flu was so deadly.
Two nonfiction suggestions for the "Books about Books" category:
The Book of Lost Books by Stuart Kelly -- Just what it says on the label, books we know about but no longer have. It's broken up into eighty or so small chapters dealing with authors from Homer on up to Sylvia Plath.
The Man Who Loved Books Too Much by Allison Hoover Bartlett. The subtitle for the book is "The true story of a thief, a detective, and a world of literary obsession."
Lastly, for the "Alternate History" category, I have both fiction and nonfiction suggestions.
Fiction:
The Peshawar Lancers by S.M. Stirling
Resurrection Day by Brendan DuBois -- a mystery set ten years after the Cuban War of 1962.
Nonfiction:
What If?, What If? 2, and What Ifs? of American History, all three edited by Robert Cowley. These are collections of essays by historians (and some authors of historical fiction), dealing with subjects ranging from the premature death of Alexander the Great to the consequences of the Spanish not bringing back the potato from the new world.
I'm not sure if they would fit under whatever guidelines the challenge follows, but I might also throw in two books by Dougal Dixon: After Man: A Zoology of the Future and The New Dinosaurs. They're illustrated field guides to two different alternate worlds, one set 50 million years after humanity's extinction, the other set today in a world where the dinosaurs never went extinct.