Q69: In the K route, Dio takes the Neostigmine gun from the Treatment Center’s safe. He is very insistent on keeping it, which seems to imply that he knows of its value.
     Does he know that it can be used to counteract a penalty? In the K Game Over, K opens the nine door, but Dio doesn’t attempt to escape himself.
     If he knows what it does, then why doesn’t he use it to go through the door? If he doesn’t, then why does he want it so badly?
     Does he also take the Neostigmine gun during the other timelines where he goes through the green door?

     No, I assume he didn’t know what kind of effects Neostigmine had. I believe he just had a hunch that the medication would be somewhat important.
     In terms of why he wanted the neostigmine gun, it wasn’t a matter of what medication was in that gun, but I think it’s only natural that you want possession of any kind of gun.
     On a side note, on the Alice route Dio entered the Treatment Room with Phi and Tenmyouji. Since Phi and Tenmyouji got to the safe first, Dio never got the neostigmine gun.