These cars the dash lights are very common to go, usually in the radio, climate control and window switches. There is no doubt in my mind the accident caused these lights to go and a faulty BCM would not cause this issue unless all back light lights on the speedometer, and what I mentioned above all stopped lighting up. My 03 sunfire I had a few years ago had the odometer light burn out after a 50 km/h impact.

The lights are all soldered in these units so it's on the insurances plate to replace whatever parts have the lights burnt out inside them. If they end up not doing so even after a fight with them they can be replaced by anyone with good soldering skills.

The remote...A Bad BCM could cause this issue with keyless not working, but it's common in these remotes for the battery clip to become detached from the circuit board due to bad solder joints. The remote hitting on the dash in the crash could have pushed this over the edge and cracked the solder. It's held in place by three different places by solder, open it up and check these.

Do you have a spare remote? if so does that one work the car? and does your power locks work with the switch?

The BCM controls the power locks, The keyless entry reciever is a box in the back of the car between the two speakers that listens for the remote commands and tells the BCM what lock/unlock actions to do when a button on the remote is pressed. If your tire pressure system is working then the link between the keyless entry reciever and the BCM is good as the keyless entry reciever also communicates with the tire pressure sensors.

And the windshield washer motor...these are pretty close to the bumper and stuff usually, So I would say the accident probably caused this and deserves a closer look for severed wires.

In any case the exterior and interior lighting all go through the BCM, So if you got any wires pinched in a wreck and shorted to ground this could very well mess up the BCM. This could be why the diagnostic determined the BCM was malfunctioning as well. but replacing the BCM alone will not fix the sections of interior lighting that are not working, but could be the culprit for the other issues.

Once this thread gets enough responses I would show this to the insurance company as well, I know the car inside and out electrically.