FAQ

It is called a "dragons tail table lamp"

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No. Sherlock and Joan are treated as unique; the Sherlock Holmes books by Sir Arthur Conan Doyle do not exist in this fictional universe.

The books' Sherlock indeed had a Dr. Watson as an assistant, and re-enacted characters appear such as nemesis Moriarty and brother Mycroft.

It is now widely known that Sir Arthur Conan Doyle's Sherlock never actually said, "Elementary, my dear Watson." However, due to its' popularization in other media, it is considered his signature phrase. Doyle's Sherlock uses the word "elementary" only eight times in canon, usually referring to his immediate deductions from the smallest of evidence (such as the dirt on someone's shoes.)

Thomas Leitch identified the phrase, "Elementary, my dear Watson" as originating from William Gillette, the American actor and director whose pionerring play "Sherlock Holmes" (1899) played for more than 1,300 performances. Leitch is professor of English at the University of Delaware, and the above is quoted in his book "Film Adaptation and Its Discontents" published in 2007. I think we can trust that the professor has done his homework here.