Both of these deaths would be under the jurisdiction of the NCIS, not local law enforcement. They have jurisdiction over any homicide involving a marine or sailor, whether as a victim or the suspect.
Cpl Patrick Kirby is wearing incorrect rank and ribbons during Alex's autopsy. He is wearing the rank of a PFC (single chevron) and the National Defense Ribbon. He should be wearing the rank of a corporal (2 chevrons and crossed rifles) and the Iraq Campaign Ribbon and the Global War on Terrorism Service Ribbon at the least.
Of Hicks had been shot in action he would have been awarded the Purple Heart. He was not wearing that ribbon.
Caleigh states Hicks may have been shot previously while saving lives because he wears the Bronze Star. His ribbon has no bronze star so it was awarded for meritorious action not valor.
Calleigh said they were able to identify the DNA found on the victim by gaining access to the Department of Defense's (DoD) casualty DNA database. When someone joins a branch of the armed forces a sample of their DNA is taken and recorded, though only for the explicit purpose of identifying the remains of personnel killed in action. This database is not accessible to law enforcement, it is strictly used for identifying remains only.
Alex says that she used a fluoroscope on the body. The device she used has an x-ray emitter in the upright silver cylinder and a large optic that collects the x-rays. In order for the device to work, a body part like a limb, needs to be put in between the upright cylinder and the optic so that the x-rays pass through the body and into the optic. Alex simply waves the device over the chest. A much larger machine would need to be used that would wrap around the body in order to view the chest.