They never explained the 'powers' or the trolls.
Why does that need to be explained? Just go with midiclorians as your answer.
The parents keep them locked up, never to even talk?
It's implied that they talk some, they just grew distant from one another.
The queen runs away and wants to become a hermit in an ice castle?
Pretty clear you missed not only the point of her character, but the point of the entire film. She was basically trained from a child to shut out everyone and everything. Being a hermit in a ice castle comes pretty natural to her. Once she overcomes this and opens her heart to others, then the winter ends.
Although predictable, the prince turning into the bad guy was a twist, but his plot to take over was developed awfully quick in his head. He friended her, fell in 'love', and then decided when she left to try and take over?
The guy was there to marry the Queen, but saw that she was some shut out who was incredibly cold, so fat chance he gets her. However the second in line for the throne is completely irrationally into him, so he makes lemonade out of lemons and then plans to murder off the Queen at some point when he marries the younger sister. I don't see why this would be too hard to come up with on the fly when those are your motives.
This post was edited on 1/2 at 6:29 pm