Regarding the box:
See the epiloge of Nicholas and Alexandra by Robert Massie.
In January of 1919 Nicholos Sokolov assisted by the tutors of the Tsarevitch, Gillard and Gibbs found the remains of the cremation attempt. At that site they collected:
. the belt buckles of the Tsar and Tsarevitch
. Empress Alexandra's emerald cross from Empress Marie
. one of a pair of pearl earrings always worn by Empress
Alexandra
. the Ulm cross presented to the Empress by her guards
. fragments of a saphirre ring of the Tsar "too tight to be
ever removed"
. the Tsars metal pocket case in which he carried his
wife's picture
. 3 small icons worn by the Grand Duchesses
. the Empress' spectacle case
. 6 sets of corset fasteners
. fragments of the military caps of the Tsar and
Tsarevetich
. shoe buckles of the Grand Duchesses
. Dr. Botkin's eyeglasses and false teeth
. charred bones with marks of acid, axe and saw
. melted bullets
. a severed human finger of a middle-aged woman,
slender and manicured like the Empress's
. a collection of odds and ends always carried in the
pocket of the Tsarevitch
I seem to recall mention also of a small vial of human fat left over from a cremation. As I recall Gilliard and his wife took the box containing most if not all of the above. They offered it to Empress Marie who could never accept the IF had been murdered, she refused it. Other family members not wanting to offend her also refused. The British royals were offered the box and they refused it as well. Eventually it was handed over to a bishop of the Russian Orthodox Church Outside of Russia. (ROCOR)
For the rest of the story, see:
http://www.monasterypress.com/Royal.html