Capt Diaz tells Private Neill to answer his questions even without counsel being present after counsel was requested by Private Neill. Under Article 31 of the Uniform Code of Military Justice, Private Neill did NOT have to answer any questions until counsel was provided as he requested. This is a common Hollywood mistake about the military in general and military justice in particular.
Once it had been determined that the deceased was a military person, even if a deserter, the military would have handled everything, including the autopsy, unless they declined to handle the case. That would normally be the case in matters involving military and civilian personnel off-base.
Colonel Bayless stated that once Corporal Webb became a deserter, she was no longer considered in the military which was why there were civilians, i.e. Jordan, helping in the investigation. As someone with his rank would know, just because a person deserts the military, they are still carried on the books as being in the military and once apprehended would be subject to Court Martial, no matter how long they had been in deserter status.