There were four libraries in the Alexander Palace. During the 30s, about 20,000 books from the libraries were sold to the US. I will try to find the source. What remains is but a fraction of what once comprised Nicholas II's library.
Yes, the building of the Alexander Palace still belongs to the Ministry of Defence. The Imperial Wing is a bit of a hybrid. The World Monuments Fund and Gleb Panfilov invested hundreds of thousands of dollars on the Family Wing - not for the benefit of the Navy, but in the belief that the building would be returned to the Ministry of Culture. It is TSM who fund the maintenance of the wing, not without inevitable tensions.
The Alexander Park and its pavilions are under the jurisdiction of Tsarskoe Selo Museums. They paid for the restoration of the White Tower and propose, shortly, to commence the restoration of another pavilion in the Alexander Park.
I am optimistic that things are moving, slowly, in the right direction. When the transfer happens, I think we will find that, suddenly, it is a fait a complis.
tsaria