Black Butler: Book of Murder

Siemens was targeted because Woodley, a businessman whose diamond business Ciel was planning to destroy, wanted to frame Ciel for the murder. Woodley killed Siemens after the latter faked his own death as a prank, using the chaos of the banquet to place blame on Ciel and prevent his legitimate business takeover.

Siemens was killed by Woodley, who had been corrupted and wanted to protect his diamond business from Ciel's legitimate takeover. The murder was committed during the chaos following Siemens' fake death prank, allowing Woodley to frame Ciel for the crime.

Earl Grey, the Queen's butler, was tasked with killing Siemens to slow Germany's financial ascent by eliminating the German banker. Simultaneously, the Queen used the situation as a test of Ciel's nerve as her 'Guard Dog', framing him for the Noah's Ark Circus incident to gauge whether he could handle the pressure of false accusations while serving the Crown.

Sebastian had secretly invited Reverend Jeremy Rathborne to investigate the murders, but at some point disguised himself as Rathborne to manipulate the investigation from within. This allowed Sebastian to guide Doyle's detective work while maintaining control over how the truth unfolded.

Earlier in the timeline, Sebastian is shown asking Rathborne to come investigate, hinting at his later deception.

One of the murders was committed by a snake trained to hunt Ciel's scent. The snake was sent by Snake, a former performer from the Noah's Ark Circus, to avenge his friends who had been killed. This connected the present murder case to Ciel's previous involvement with the circus.

Doyle realized that no single person could have committed all three murders due to the physical impossibility of being in multiple places at once during the timeline of events. His observation that three separate murderers were involved became a key clue in unraveling the case.

Ciel invited Snake to live at the manor as a strategic move to win Snake's trust and prevent future assassination attempts. By bringing the potential threat close to himself, Ciel could monitor Snake and neutralize the danger of another circus-related attack on his life.

The Queen suspected Ciel had omitted information about the killed captive children from the Noah's Ark Circus in his report. To test his loyalty and obedience, her butlers orchestrated the entire murder scenario at the banquet to see if Ciel would remain loyal under false accusation and pressure, essentially testing his worth as the Queen's 'Guard Dog'.

Sebastian was killed that night as part of the complex murder scheme orchestrated by Earl Grey. The kill was part of the overall plan to create chaos and place Ciel under maximum duress during the Queen's test. The specific details of exactly who physically carried out Sebastian's killing were part of the larger conspiracy.

Doyle noticed inconsistencies in the case that didn't add up, particularly regarding the three separate murderers and the political motivations behind the crimes. His detective instincts led him to discover that Rathborne was actually Sebastian in disguise, and that the Queen had known the true culprit (Earl Grey) all along.