1-Momoko confessed for 2 reasons
- -She was unsure
- -She probably was following Niiya and heard him talking about the Yuuko-san ghost and mistook it for him loving the sotrries more than anything, but he explained very clearly that he loves Yuuko-san
2-It was Yuuko who followed him all over the place when she noticed he stopped seeing her, she was attached to him for some reason, they met again in the corridor out of the blue, which can suggest that she can't seem to escape seeing him. However it is strongly suggested when Kirie was pushed away from Niiya that every event in that short time (probably a week or two) was all the doings of Shadow Yuuko.
3-Kirie did not really joke about replacing Yuuko, she would be easily able to do it since she looks nearly exactly the same as her, with the certain area exception.
I don't think anyone noticed it, but Kirie browsed through an old photo album in the P.I.C, in that picture there were Yuuko-san, her
twin sister, and their little sister.
I hereby announce a new theory, peek into the spoiler at your own despair!
Shadow Yuuko is indeed as you probably guessed, Yuuko's twin sister, it is likely they both died nearly at the same time, probably for different reasons, however it would appear Yuuko died first and was never found, she is believed to be the disease victim but I have a feeling it's not quite that. Shadow Yuuko is all the hatred Yuuko had + Her sister's grudge, it would appear Yuuko of the two twin sisters was much more popular, which caused her sister to hate her and envy her, that could explain why Yuuko was locked away in that basement, probably by her own sister, who took over her place, and was living her life until the plague hit the area.
It could be possible that the Yuuko we know is in fact her sister who locked her away by the small shrine in the basement and she managed to get out of there, but she had no strength to overcome the next obstacle and eventually died holding a grudge.
Yuuko's sister wa living her life until she died, and Yuuko's grudge made it impossible for her to move on so she remained as a ghost, however some of this could also make sense if the Yuuko we know would be pushing her burdens constantly onto the real Yuuko, which could be why the angry Yuuko is acting now more actively than in the past as far as we know.
Shadow Yuuko is trying to do something, probably to confront herself with the other "fake' Yuuko, but for that, she has to regain her memories, which is why she interfered so much recently allowing small facts to surface and often interacting with Kirie because she was an obvious obstacle.
Next episodes should clear this up, but I wonder if they will manage to do it in the short time we have left.
Anyways, this is surely an excellent show, wish I could read the light novels but I'm too lazy to read them online if they are translated.