I come from a Noble Princely line descending from Prince Yanbulatov Shemanov of the Crimea and thus Tarta lines.
What you need to understand about the title of Prince in regards to Russian nobility is that Prince is not akin to a Prince within the UK. The title of Prince is a stand alone title, as it was in many of the Germanic countries and it is more akin to the title of Duke. Differing styles of address also denote different ranks of Prince's within the Russian Empire, however this was often vague and a lot was lost in translation e.g. His Serene Highness (HSH) is a higher rank then His Illustrious Highness (HILLH).
Also you must understand that titled nobility where not the only kind of nobility and you could gain inherent nobility within the Russian empire from service to the empire and by obtaining certain grades. My Great Grandfather for example, who held the inherent title of HSH the Prince, also held the military rank of Major General. These such ranks where denoted by styles of address such as His Excellency.
However back to some of the questions at hand...
To answer the question regarding land within modern day Russian. Most surviving descendent's from princely lines now live outside of Russia due to there family's escaping during the revolution. From experience I can tell you that when you ring up the Russian embassy in regards to retrieval of land or enquires to that subject they put the phone down on you or ignore all correspondence, however within Russia itself some families have managed to claim back land stolen from them during the communist era.
In regard to the title of Prince, the title of Prince is the highest noble title (not rank or style) that can be held by a noble who is not of the imperial family. The title of Grand Duke is a higher title. However a lot of the Prince titles date back to a period where what is now known as Russia was split, the Rus and the Keiv lines. Some, like my own, went back through the Ottoman Empire at some point and before that to separate Princely states or, again like my own, to be traced back to descend from a royal line. Or the title was translated over from other such title like Khan.
Because many titles outdated that of the Russian Empire many titles had there own rules and caveats attached to them outside fo the code of Russian nobility. The Romanov family are examples of this in themselves in regards to there rules on monastic marriages and claimants to the throne. My own family for example holds cascading noble title, hence why I am a Count (Graf) and not a Prince, as I am superseded by an older brother and still living father. The right to use my surname is also an honor which is not automatic but must be bestowed by the head of the family, which is my father, which in turn brings the right to cascading title. However I have known some Russian noble families follow a more central European approach to title and inheritance where all cadet members of a family hold a title, as of Baron or Count, while the head of the family may be distinguished by a higher style (and rank) or a higher title).
In short the title of Prince within the Russian Empire was a complex one and not governed by a set of hard and fast rules or laws.
It is worth noting that all such titles still stand and are still recognized under international law.
