Context dependent memory applies to music as well. Unless you can convince your proctor to play music during the exam, I would power through it without.
I brought enough to get the proctor's attention. He saw my bag, started laughing, and said, "guess you won't need that sharpener."
The instructions say to bring 4 (I think), but most of the people around me had 8+
It depends on the proctor, but I have heard of people getting kicked out for not putting pencils down immediately. It would be in your best interest to get used to having everything bubbled in before your pencil needs to be down and time is called.