Sorry for taking so long to respond. I wanted to focus on the new version of the game's release with the Nao mission, and also Dota released the Battle Pass :P .
For main post: That mansion used to be a whole self-restrained horror mini-game, where Hana (with her old faceset) explored a haunted mansion alone. Since then though, both the plot and Hana's personality have been rewritten from a scratch retconned so much and my techniques and tools for creating the game been upgraded so much, that it would take more work to fix the mansion than to recreate it completely. Right now I'm not sure what to do with it. One idea is to create a mission exclusive for Hana if the player has romanced her enough, which will also be a self-contained horror game, but with the modern plot and her personality in mind. Another is to keep it in standby, for one of the class girl missions. A third idea is to scrap the entire area entirely, and create a new area with a new event/boss, like the rat village or the zombie village. I'm open to suggestions.
For Edit 1: Well, Hana is not exactly "bound" by monogamic limitations. In her head she is the hero of the story, not you. She and Gouki will just remain friends (unless you follow one of the other girls).
For Edit 2: The quest can be finished as soon as you reach Floor 6. Depending on how you choose to finish it, more quests might unlock for later floors, but the first part is entirely done on floor 6.
For Edit 3: The girl you are seeing is Hana's old face, before it was replaced. I have changed almost all of them to her current faceset, so do tell me when you find one of them.