Are there actual historical instances, in the late 19th or early 20th century Anglosphere of any of the following:
a murder solved by an amateur detective
a murder at a classic Agatha Christie setting, such as a gathering of aristocrats and well-to-do at a dinner party
a butler murdering someone in the household
An interesting case you might want to look into was the murder of William Rice whose death lead to the founding of the prestigious Rice University.
In 1900 William Rice was chloroformed to death by his valet Charlie Jones. He conspired with a lawyer, Albert Patrick, to embezzle Mr. Rice's estate. Suspicions arose when a bank teller noticed a large check with Mr. Rice's signature written out to Mr. Patrick, but with his name misspelled.
Captain James A. Baker (Rice's attorney and grandfather to president Reagan's Secretary of State James A. Baker III) ordered an autopsy which found evidence of poisoning.
After being discovered, Jones turned on Patrick in order to get immunity. Patrick was convicted of murder and spent four years on death row at Sing Sing Prison before having his sentence commuted by Governor Frank Higgins in 1906. He received a full pardon from Governor John A. Dix six years later.
Rice left the bulk of his estate to the founding of a free institute of higher education in Houston, Texas which later became Rice University.