I made an account just to reply to this text just because it was really... poorly thought out.
1. her recollection is of key moments, not solely what happened. Him being drugged, and her trying to stabilize him, lasted those 45 minutes.
2. The letters were an incentive to murder. Your point that the letters HAVE to be solely historical secrets relies on the belief Tozu is a neutral observer who doesn't twist the truth. He is not. Tozu's goal is to aid people in killing, and if that means twisting rules, making deals with the students, hiding key information, OR giving someone a heads up about where weapons are stashed... then he'll do it. Tozu is on the team of the blackened.
3. If we know that the drag racer has lithium batteries in his room, it then logically follows that the ultimate marksman has weapons. Not that far of a reach at all, and Desmond's letter seemed to confirm that when it stated "weapons in hand". We also don't see the picture on his letter, I believe, which may have shown where the weapons were.
4. The students literally make it a point that they don't exactly know when she accessed the items, but that it doesn't matter because she is the only one who had the information to even know to search his room anyways. There couldn't possibly be anyone else who had done it, so filling in the last gaps was not necessary. They overtly state this.
5. Doors can, in fact, lock themselves once closed. They are pretty common actually.