1: Her recollection of the moment specifically shows him rousing himself after just a few attempts. There wasn't any visual or said moment where time passed that long on her just trying to wake him up. And it just wouldn't make sense that she'd stay that long for that. After 5 minutes of being unsuccessful, any rational person would try an leave to get help, to find out the door was locked, and the entire flashback would have played out differently. Besides, if she did just stay in that room doing nothing but trying to rouse him, then she's just a moron which the story doesn't depict her as. And don't say she was panicked either cause that would imply further she'd try and go for help sooner.
2/3: Literally all of the letters are about past events. True, Tozu could have twisted the rules for that one letter, but the characters in the story wouldn't have known that. They would assume the pattern is the rule, and the pattern established is that the letters refer to past traumas. No one even knew the Racer had lithium batteries until the trial, except for Eva. Not even the Racer knew. There's no reason for the characters to assume foul play. Also, the picture thing doesn't work considering they never showed what the picture was. If the picture did indeed show where the weapons were in the room, why didn't the writers show that to the players? Don't make up fanfiction to excuse bad writing.
4: The fact they can't prove how and when she got the items means she could easily spin the narrative that someone else knew the information and got the items instead of her. Knowledge of an item doesn't mean she took it, especially without definitive proof she did. That's not how you win court cases, that's how you lose them. There needs to be definitive proof that she nabbed the items from the room, otherwise the logic feels faulty.
5: Yeah learned that myself from the comments, but that doesn't explain when or how she got the tools to turn the doorknob. Again, more faulty logic.