Mark,
First off let me be picky here..., because I am one of those people that is picky on using proper terms. (fins, not flippers..., that sort of thing). The reason I mention it is because if you find it, you'll have to enter it in court and I've seen defence lawyers try to throw the odd curve here.
We are all victims of the CSI world. We, as divers DO NOT collect forensic evidence, we collect physical evidence. The water and soil samples you mention are physical evidence from the scene. Once the scientists in the lab do their thing, their findings are the forensic evidence. Even a latent fingerprint at a scene is physical evidence until the pros make a match at the lab.
So the question should be.., how much physical evidence can a dive team collect and preserve in zero viz.
Let's be honest.., zero viz, cold water (thus gloves) are we going to find hair and fibres not currently located on the body? No of course not. We just cannot physically do it by searching. Now if it a big enough case...., a small suction pump, a grid pattern and 'viola', a minor excavation where the pumped water from each grid is filtered through fine sheeting and there are your hair and fibres. Do you do this for every sudden death where 30 people at the beach saw the person drown.., no, of course not. But a huge scene, potential serial killer..., maybe.
bare minimums for physical evidence at every scene?? (just off the top of my head and before my morning coffee so hopefully others will throw more in)
-location, location, location (where the body was located in relation to a fixed point on the shore, or GPS.
-Depth (I take it at the victims head)
-position of body
-physical condition of body (I've had to talk an ME through this one after the vic, 6 months in the water, literally fell apart between the bottom and the morgue)
-direction of body (if possible) I use a compass bearing from the head down the body or in relation to any continuous, non-tidal current
-temperature of water
-body (bagged on the bottom)
-water and soil samples
-a search of the area (10-15 foot radius) looking for anything else, clothes, shoes, jewelry, signed confessions.., that sort of thing
I can't really comment on your first part of the question regarding the evidence chain and communication with LE and medical examiners, because I'm in a little bit of a different situation than you guys and cannot give a proper comment on this.
If you lack knowledge in the processing of the evidence, I recommend you try to set something up with your lab weenies.., and get it straight from the horses mouth. They are also the people who can give you the best advice on how to preserve anything you collect as they'll tell you what condition they want the items in when they get them. Most I have met love to talk about what they do and are more than willing to do anything to make you (and their) job easier
Great topic for discussions Mark, I look forward to reading other responses