I never understood what's even the point of these things.
Imagining things and trying to connect with others by sharing them, maybe?
Or perhaps just a thought exercise involving something you like.
She is Faggotsuki's daughter from the future and kills herself because of the implications of her legacy.
I think that's just the way the character was designed.
madotsuki was raped
I think it's pretty obvious that something bad happened in Madotsuki's life. There are so many scary events and little hints that can point to a number of things. There are themes of rape (FACE, Bloody Touching Monster), traffic accidents (Shitai-San, Monoko), and just a lot of other stuff that doesn't seem normal. Why does she never leave her room? What is with all the Aztec imagery, even on her carpet in her room in the real world? Maybe she has some kind of illness or she's insane, which could explain why she acts the way that she does, and why she has such vivid dreams (as well as why she seems to be comfortable with all of it!). Or, another thing I've considered, is maybe this game is supposed to have a deeper meaning? Think about it. There are so many odd and surreal things in Yume Nikki that kind of feel out of place sometimes. Takofuusen. Uboa. Mars-San. The Torinigen Party. Maybe KIKIYAMA isn't trying to tell us something about Madotsuki's world, but ours? Maybe the reason why all these things exist is because it all has a deeper meaning. Yume Nikki is such a complex game, there probably is some sort of meaning, whether it be addressing the characters in the story, or about real life, but… what is it?
Madotsuki raped herself.
Rape Madotsuki'd itself
Madotsuki is a test subject sent in by sRAM999, a clandestine group with various connections in inter-galaxy business. She was sent in to spy on humanity, but she betrayed her employer by falling in love with Poniko, a human child who actually didn't give a fuck about Madotsuki so it was onesided who Mado used to hang out with in elementary school. Hearing of the betrayal, her former employers sent out drugs to her brain via nanobots to immobilize her and capture her for information.
Yume Nikki is set in the stage where she got drugged, hiding out in an abandoned apartment, scared for her life. The only thing she can do is wait it out before she's semi-paralyzed. Her dreams reflect her alien background and her drugged mental state, with the Tori's being Madotsuki's former comrades. Masada is one of her former comrades and her dear mentor, killed out by sRAM999 (a genius anagram of Mars666) because they found he was raping humans he captured as test subjects, rendering them unpure for research. Uboa is Poniko's imminent capture and alien transformation/experimentation. Kyuu-kyuu represents the various fun things Madotsuki got into when she came into the human world due to her naivety (even though she had a Earth tourist guide), which she regrets heavily.
Her getting kil is basically a way to end her suffering and die a proud "human" being before she gets paralyzed, insane and tortured to death.