You give a lot of good info, but I must take exception to one of your comments..."Never move your car unless told to do so." If your vehicle is blocking a traffic lane, and is movable, 'specially on a freeway, you are much better off moving it to a location well clear of any traffic lanes. Leaving it blocking a lane will just about guarantee more collisions, possibly doing more damage to your vehicle, and injuries to all. Take pics if you can, and if you happen to have a can of spray paint in your vehicle (the bright orange spray straight down type, availble in most home improvment stores, is best), mark the location of at least two tires on each involved vehicle before moving them. IF you can do that without standing in the lane with your back to traffic.

When exchanging information with the other drivers, be sure to record not just the license number of their vehicles, but the VIN number too. The VIN identifies THAT particular vehicle, the license plate will only identify the vehicle that plate is supposed to be on. Many people own more than one vehicle, and it is not uncommon for them to put the wrong plate on the wrong vehicle. Rental companies often do not even know what plate is on any of their vehicles, they go only by the VIN and/or a company assigned number. Ask them anything about a license plate and they don't have a clue.

Most important of all is to remember that standing in the middle of any road, especially a freeway, is one of the most dangerous things you can do. DON'T DO IT! If the vehicle can not be moved from a lane, get all occupants out of it and move them to a location well clear of the lanes, even if it is pouring down rain...