Which materials I can find in the Russian Archives for family history? For example, family books, pasports, church records?
There are many docs. Most of them are located in the corresponding regional state archives. For the success search you have to know the territory name, church name (typically) and dates.
There are fonds, where I can find, when Dmitrij Krestovozdvizhenskij leaved Russia?
There are three ways.
1. If he leaved Russia during Civil War in 1917-1922 than most possibly his name will be in catalog at Russian State Archive. I already mentioned it to you before and I remember that I promised to look over this catalog but I simply don't have time right now to visit this archive, unfortunately.
2. When he arrived somewhere it must be recorded in passengers lists or immigration records. Ancestry.com or a similiar web-site might help you.
3. If he leaved Russia before 1917 then there are possibly should be a record either at customs service (regional archives, Russian State Archives, Russian State Historical Archive) or, possibly, in docs of Ministry of Foreign Affairs of Russian Empire. There is a special archive called the Archive of Foreign Policy of Russian Empire. It is located in Moscow and is a part of Ministry of Foreign Affairs. I do not know about what information is stored here. AFP of Russian Federation stores docs starting from 1917 and AFP of Russian Empire stores docs before 1917. I did research in the Archive of Foreign Policy of Russian Federation and work here is completely different from any other archives in Russia, which are belongs to the Russian Federal Archive Service.
P.S. I also interested in same type information (when my ancestor leaved Russia) before 1917 but to be honest, right now I don't have any exact idea how I can find it.
Again, you have to clearly state a clear goal, for example "I want to find a birth record of .....". Then you can find where (with advice of this board users) this information at least have to be stored. I understand that you are in general looks for a great amount of information but it is crucial in family research in Russia to divide your search in small parts. This is how it works in Russia. The biggest problem in Russia is that due to our history the archive docs were moved from one archive to another and also due to change in region borders some docs might be stored in a regional archive associated with regional borders, which were in past.
Feel free to ask questions. I will be personally happy to help you!
P.P.S.: Maybe you noticed that in St. Petersburg address book of 1909 and 1910 has a record of Arkadiy Ivanovich Krestovozdvizhenskiy, Podpolkovnik (military rank lower than Colonel), dies in 1909/1910. His wife Anna Timofeevna.