No. Time-travel plots causes a lot of mess.
The reason it was snow in Seanchan was that it was on the other side of the world. So summer in Cairhien is winter in Seanchan.
Nakomi is an avatar of the Creator, sort of like Shaidar Haran was for the Dark One, but the Creator does not take part as...
Yes, I would suspect that in some way, the Three knew that Rand was still alive because the Bond was still intact. All the signs point to this, they do not seem to grief like others who have lost a Bondmate, and they never even hestitate about whether he is really dead. I seem to recall also...