You can play any of the modes here, but if you want bots, you'll need to go to Game Settings < Bots, then configure as you wish. You can pick the amount of bots, how difficult they are (with a "mixed" mode, which I feel portrays real lobbies correctly) and other things.

Hair Attack: Kayako's primary weapon is her hair. She used it to kill her husband after he killed her and she uses it to strangle, blind, or bind others. In the game, she is also revealed to stab her victims with her hair.

In The Grudge, Takeo is instead hanged by the neck inside the house. It is implied that he hanged himself. However, in the Director's Cut version of the film, he is seen hanging by Kayako's hair, indicating that she was responsible for his death, thus making him the first victim of the curse.