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?
Why couldn't Eve make the Ultimate Being just by manipulating Kiyomi's own egg cells and then having sex with Toshiaki? Why did she need Kiyomi's liver implanted in another human female in order to create the proper conditions for the Ultimate Being's birth?
Since all mitochondria is passed down from the mother, how do Toshiaki's mitochondria have a Y chromosome?
Everyone at the opera spontaneously combusts except for Melissa/Eve, Aya...and Aya's date. Why is he spared?
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).
It's never directly stated but as mentioned above it's implied to be mind control. At one point, Dr. Klamp was mentioned looking for HLA lists, and you find one of them at a later point in the game. HLA lists are used for determining if someone is a match for things like bone marrow / blood transplants. Therefore, it's likely that Dr. Klamp found enough HLA matches to make the slime that wouldn't reject Eve's baby, and Eve used her powers to control them to arrive at the concert.
Why did Aya get into carriage with Eve instead of just shooting her?
Aya was still uncertain about her own powers and subconsciously followed Eve to find out more about herself and what Eve was planning. This is before Aya knew what Eve was truly capable of.
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.
Besides Rule of Scary, is there any logical reason for Eve to have a huge and nasty pregnant belly when she's still carrying the Ultimate Being, considering that it's not much bigger than the average infant when we finally see it in all its glory?
It was pretty large when you see it, normal babies are tiny. Add to that the wings.
It's the middle of Winter, in New York, yet most of the characters aren't dressed for the cold. The little boy wears shorts both indoors and outside, and Maeda spends the night sleeping outside, in nothing but his suit.
Chalk it up to oversight and/or laziness from the dev team, but December is the start of the winter season and the weather doesn't get truly cold until mid January, so it's possible for the characters to not be too uncomfortable by the cold as long as they're active. Aya does scold Maeda for sleeping outside in the cold weather though.
Why is there a burning barrel inside an apartment? Even if the furnace failed, this would cause certain problems with smoke and carbon monoxide.
There could have been windows we didn't see that would allow the smoke to escape. The apartment room itself looks very worn down and was probably being inhabited by a homeless person who also started the barrel fire to keep warm.