I’m sure they searched it before entering the school because the shotgun is mentioned on the police dispatch along with the rifle 15 minutes after they got there.
In the tape that shows them in the trunk in the dark, they are emptying the chamber and clearing the shells and then the csi tech takes the shotgun out and with him. So they weren’t in the trunk at that time just finding it but to take it with them back to the lab.
That wasn't Lanza's car...You will notice that the passenger side of Lanza's car is facing the school...You will also notice one of the helicopter shots was from the passenger side of the vehicle...You will also notice that between Lanza's car and the school there are no trees...Then, you may notice that on one of the helicopter shots, the trees are blocking a clear view of the trunk of the car with the shotgun in it...Not the same car...