It's done to show other agents disdain for Clarice, but to think that she doesn't already have an FBI windbreaker, just isn't believable.
Two bodies, found at the same location, killed at the same time, is not, by definition, a serial killing. They would need to be separate events occurring at different times to be considered a series.
There is no way that an FBI agent would know that there is no water in the lungs of the victims without getting that information from the autopsy.
At 1993 there was no way for an FBI agent at the field to identify a body by its fingerprints, that were a lab's job.