Thank you as always for the cultural notes at the end of the chapter!
"Kokeshi" is also a pro wrestling move. It's a headbutt where the user stands stiffly like a kokeshi doll and then tips over onto their opponent.
We still don't know. In the final panel Negishi-kun gives us a possible answer: self hypnosis. And Mikurube-san insists that she would NEVER think of such things by herself, a real "she doth protest too much" situation if I ever saw one.