This may be a 1959 novel (1960, according to ISFDB) by Alan E. Nourse called Star Surgeon. The background is that every race in the star-sprawling republic/confederacy/whatever has a specialty that benefits the other races. Earth's specialty is medicine. To prove that Earth is ready to become a member, a humanoid alien, Dal Timgar, is sent to one of the training schools that Earth has dedicated to training the various specialties of Earth's Star Surgeons. Here is a synopsis of the plot:
The adventures of Dal Timgar, born on a planet of a distant star, who attempts to become a qualified physician of Hospital Earth. This exciting science fiction story is a selection of the Junior Literary Guild. When Dal Timgar, of all his medical class, was denied assignment to a general practice patrol ship going out from Hospital Earth to serve the medical needs of the Galactic Confederation, it seemed to him that his eight years of study in the great medical center of the galaxy had ended in failure. He had worked hard and stood at the head of his class, but Dal was different from his medical colleagues in one important way. Born on a planet of a distant star, he was the first son of an alien race to attempt to become a qualified physician of Hospital Earth.
The teens (human and alien) were in their early/mid teens and were students in some kind of special school. The alien teen and human teens were in a specialized medical school.
The bad guy was an older human teen non-student who was bullying one of the students The bad guy, who did not want an alien representing Earth as a Star Surgeon, was one of their highly esteemed teachers and the Head of Pathology, which wears black cloaks. The graduates who passed their internships were granted a Star clasp that held the cloak in the color of their specialty. Everybody knows that a person wearing a Star was an accepted member of Earth Medical Corps. Surgeons wear red cloaks.
The one that got killed was trying to stop the bully. Well, sort of. The Head of Pathology, who wants to prevent Dal from earning his Star, has a heart condition. He was about to succeed in keeping Dal from earning his star when he had a major heart attack. The cardiac condition would be fatal if he was not operated on immediately. The only surgeon available is ... Dal Timgar, who the Head of Pathology has always believed is unqualified to wear the Star. Dal chooses to operate on his nemesis. The operation is a success.
The story happened on earth. Well, some of it does. The medical training takes place on Earth. After graduation, the students are given a ship and a route, somewhat like a doctor (or priest) who "rode" a circuit from town to town in colonial times. The end also takes place on Earth.
The alien students were the children of diplomats. It's probable that Dal was a son of a diplomat. The final test for joining the Confederation, which was never mentioned until after Dal Timgar earned his star, was Earth's willingness to share their specialized knowledge with other races. When Dal earned his Star, Earth passed the final test and was in the process of being admitted as a member of the Confederation when the book ends. There were a few days of diplomatic speeches which the teens were allowed to forego because they were medical specialists, not diplomats.
