What is so special about Kiyomi (and Maya Brea) that Eve forms inside them? Are they special in some way, or is Eve inside everyone and they were in the wrong place at the wrong time?
Toshiaki was under Eve's spell, but still, what was his original plan with his wife's liver cells? He was surprised when they started growing. Was he going to look at them forever?
So, why did people go to the concert? There were news of people burning to death in the opera and how Melissa turned into a monster. And she even appears on stage as a monster! Yet nobody ever thinks "You know what? This would be a very bad idea". I mean, even if they didn't know about the opera incident, I'd say that a woman turned into a monster who can float in the middle of the stage is a warning to get the fuck out of there.
I think there's some implication of mind control being involved - the same as Aya being drawn to the opera (yes, she says she saw an ad in the paper, but I think Eve still claims at one point to be responsible for Aya being at the opera).
Why did Aya get into carriage with Eve instead of just shooting her?
How did the phone work in the hospital when the power was cut?
landline rely on their own power, but the other question is why all the power is still on after the evacuation.
That's easy. One, even if the outside power was cut, many major hospitals have on-site power which activates automatically. It won't run forever, but it's enough to keep things going. Two, there were still thousands of people in New York City after the evacuation order happened. (There were a couple thousand cops, at least; it's bizarre you only see like, six guys from #17) There were still hospital staff in the building when Aya arrives - she finds one or two torched bodies courtesy of Eve, and Aya encounters some very alive doctors that she rescues from mutants. When you next see the doctor, she exclaims that she needs to see if anyone needs medical assistance, then rushes off. Moving critically injured patients is difficult; there could have been an entire ward of people Aya just never encountered since she only explores a small portion of the building.