The song Barry sings to Archer while he is in his coma is called Las Mañanitas. It is a traditional Mexican birthday song, usually sung early in the morning to awaken the birthday person.
The childhood recollection that Cheryl has about a servant snapping, burning the house down and murdering survivors with a hatchet is a reference to the 1914 Taliesin massacre. The killings were carried out by Julian Carlton, a disgruntled servant who tired of abusive treatment by the residents of Taliesin. Taliesin was designed, built and lived in by Frank Lloyd Wright, who happened to be out of town the day of the killings. Otherwise, he might have been one of the victims.
While Cyril is tying up the guards, Archer calls him Irving Klaw. Klaw was a photographer and early seller of bondage photography, often of his most famous model Bettie Page.