The theory that Inori and Overdose are Carol's children are at best speculation cause no where does either endings imply they survived. There's also the fact that Inori is pretty much a dead ringer for Mana, which leans more towards her being a sort of manufactured clone than Carol's child. Things like their dual toned hair does not explicitly imply blood relations and could simply be a design choice by the creators.
Actually, I don't even recall if it was said that she carried twins, except for that fucking disgusting void
Even during the big reveal she only used "children" when referring to the ones that have died and "child" otherwise.
Anyway the VN was exciting and enjoyable. I kinda wished the plot didn't closely intertwine with Guilty Crown's events at points so that it could stand alone as a Nitro+ VN but alas. There's even a continuity error when it's shown that
For those who are curious, here's some spoilers of events that intersect with the anime:
As for the Three Ghosts of Christmas:
Spoiler for Past - Major character spoilers:
Past's identity is none other than...
I shat bricks when her identity was revealed during her final moments.
On an unrelated and un-spoilery note, Yuu keeps up the A Christmas Carol naming farce by calling himself Jacob Marley.