why don't you tell me what you would change about what I wrote if it were a crime scene, and we can go from there
There is no right place to start with what you said, Crime Scene or not.
If you're asking what is a proper response to this situation? That question can only be answered by knowing what the scene commander knows when the first diver hits the water.
Among the thing's I'd have to know:
Do we KNOW we have a victim?
Do we have a witness?
Do we know when the car submerged?
If so, when exactly what is my timeframe?
What assets do I have (both personnel and material) and how long before they arrive?
But what is wrong with your response?
1. Communicate to the surface that you made contact and to keep tension on the line holding you in one place
Absolutely a must. Most public safety diver fatalities begin with a slack tether. Hopefully, the car, and your tender are positioned so that you have a minimum of rope adjusting to do as you perform your initial search, but keeping the rope tight while moving while searching a car in a current in 0 vis isn't as easy as it sounds, and you really don't move like an Olympic server, as you're in a drysuit, ffm, and wearing 20lbs of lead. And do you have any clue where to start looking for the car in the first place? Positioning has been known to be adverse, sometimes. And lets not even get into if there are any large obstructions in the way of the recovery.
2. break the glass and look inside -- a person in the car breathing in an air pocket would be likely to grab your arm
I see from your profile that you are a cave diver. Ever been silted out? Ever looked into a car that is underwater in 0 vis that is silted out to see what's inside? In a current? Same thing, but in a current. What kind of debris is in the car? Are there books, toys, CDs and a bunch of other crap floating around everywhere? The only way you are going to look is with your hands. If you want to "look" into that car, you're going in. Which window are you going to break, because it's going to matter.
2a: found someone? call for help
Found someone? Alive and conscious? I'm not calling for help, I'm giving the victim a regulator, and probably calming his ass down so he doesn't kill both of us, in that car in 0 vis, underwater. God, I hope he doesn't think I'm an alligator. Hopefully, my communications don't LOS when I enter the car and I can actually talk to my team still. Can I even fit a third person in this car in 0 vis, underwater, in a current? Supposedly, I'm trained at this. Would another person help or hurt the situation? And, BTW, underwater communications aren't exactly sprint clear, and there tends to be lots of ambient noises, buddy phone noises, and other distractions. Communications under this type of situation is not trivial.
3. stay on the upstream side in case there toxins being released from the car
Ummm. If you're searching the car, you're not staying on the upstream side. What if your victim is on the downstream side? How likely is that, in a current? You can't do half a job and call yourself a professional. You're going to get contaminated on this call. the fire department has excellent decontaminates, and I can usually make a couple of bucks making them pay to hose down my divers. For some reason, they love this.
4. when search is complete, make a brief excursion to the downstream side to check for any bodies
Yeah, might as well take a brief excursion while I'm at it, gotta get at least an hour on the clock. You gonna pull the car?
total time: roughly 2 minutes (after finding the car)...why would you be in a hurry?
I agree. I totally carry a couple of beers in my BC just in case of the odd time out.