Below spoilers up to episode 10, read at your own discretion.
Stone (or "Birthstone" directly translated)
First mentioned in episode 1 when it got accidentally "absorbed" by the FL when she was young, giving her the ability(or curse) to dream about the future if she sleeps at night. Based on what I read, she will turn into one of the animal in the Chinese Zodiac if she attempts to change the future. So she has 12 dreams or transformation before she goes into a coma forever (like in the beginning o the show I guess). I am not too sure if the same will happen if she doesn't attempt to change the future - but I reckon it should be the same. More about it is revealed in episode 8(see below "Book"). It was assumed the ML can neutralise the effect of the sleep curse because of his war killings (or because he is the true love?). We confirmed in episode 10 that the FL's father died because he used up his 12 chances to see the future.
Brother
ML believed that his brother was murdered and thus when into the palace to investigate (and saved the FL in the process). The ML went to investigate because of a letter he found in the brother's belongings related to the attempted kidnapping. The ML believed they are linked to his brother and thus suspected the FL had something to do with his death. In episode 6 we also learnt that the brother purchased some high-end cosmetics the day before he was killed. I re-watched the episode and learnt that it is the same stuff that the 2ML used in the ankle bell the FL wore. In episode 8 we learnt that one of the kidnappers was sent to spy on the ML.
Book (or half a book atm)
First seen in episode 8, apparently it is a "Book of life and death" belonging to the FL's father now in the hands of a hooded-guy. It described the Birthstone as the "Divine Stone of Heaven & Earth" and can resurrect the dead. It emits a strange glow invisible to the naked eye when the future it predicts is altered. The glow permeates into the air and causes hallucination of human morphing into animal. This other half of the book seems to describe how to control the stone thus the hooded guy wants to get hold of it. The other half is in the hands of an old guy who escaped.
Based on what we seen so far, there is a chance that the brother didn't die and he pretended to die when trying to get the book in order to resurrect the lady on the icebed. He was trying to kidnap the FL probably thinking that she knows where the stone is since he knew the other half of the book is not with her. So it is not really complicated and hope there is enough contents for the rest of the drama.
I am watching the drama with Chinese sub so the above is based on my own translation, my apologies if it doesn't make sense.