Soames is a professor at an unnamed British university, probably Oxford or Cambridge, who basically waylays Holmes and Watson on their vacation/research trip to ask for their help. Holmes's reputation clearly proceeds him. Soames fears that someone has seen a copy of a test he's administering the next day and is worried about a cheating scandal. If that's not bad enough, the test is also a competition for a major scholarship. Soames spends much of the story in a low-level state of panic and he begs Holmes to hurry up and solve things already more than once. Holmes ultimately saves Soames's butt, of course.
It's like his parents wanted to lock him in to a life of domestic servitude. Bannister is, of course, the manservant/butler of Hilton Soames. Bannister spends most of the story attempting to cover up for the would-be cheater, Gilchrist. Turns out Bannister was a servant for Gilchrist's father and knew Gilchrist as a child. Bannister's actions speak to the importance of family ties and loyalty, and Bannister is ultimately able to convince Gilchrist to do the right thing.
We never learn Gilchrist's first name, though we do know that he is the son of Sir Jabez Gilchrist. So he might be Jabez junior. Gilchrist commits a crime of opportunity when he sees the test on Soames's unguarded desk. He starts to copy the exam, but is caught by Bannister, who hides him before Soames returns. Gilchrist feels guilty about his actions and decides to drop out of school and accept a job out in the British Empire. Before this incident Gilchrist was hard-working and an excellent student, which goes to show that pretty much anyone can commit a crime of opportunity.
Ras is an Indian student who is among the three suspects Holmes has in the case. Ras is described as sort of nervous and overly anxious, though not a bad student at all. Though the ambitious Ras might seem a likely suspect, Holmes rules him out on the basis of physical evidence found at the crime scene. Many Indian students came to England to study in the late nineteenth century, which is of course when India was still part of the British Empire. The Indian students who studied in Britain often returned to India to work in various professions, from medical to legal to government service.
Miles is a slacker student who is smart but isn't motivated to work. Unfortunately for McLaren, he was without the aid of the internet and had to study the old-fashioned way. Miles appears to be a surefire suspect in the cheating case, but as all good detective stories show, the most obvious suspect is never the right one. Miles holds up that cliché for us.