Your guess is as good as mine, but typically games like these have the scenes split up by the boss phases, with the scenes usually getting more graphic and/or aggressive with each phase, to also convey the boss's impatience.
that would be the Kitsune I think, from the same map as the Oni (character next to the empty room). The Kitsune appears only during the day in that same map! So you might have to choose the Oni map and complete it again
Should be the kitsune.
Every level has a 50/50 chance to give you one of two monster girls as an enemy (with a few exceptions, where the level only has one enemy or two enemies appear at once).
So you just gotta get lucky to get the kitsune as an enemy and beat that stage, while she's the enemy.