Does Russia provide radar coverage and flight following services over its entire territory?
Not all countries publish the exact radar coverage, as it is sensitive information. But, if the flight over Russia is IFR (controlled), then the answer is yes, regardless of the remoteness of the area.
The services and limitations can be found in any country's AIP, and the Russian AIP is publicly available. By checking GEN 3.3:
1.3 Radar service is provided at all phases of control service indicated in para 1.2.
and 1.2 basically covers all phases of controlled flight:
1.2 The air traffic control service is divided into:
a) area control service - the provision of control service for flights of all aircraft in CTA (FIR/СТА), except those indicated below in items b) and c);
b) approach control service - the provision of control service connected with arrival and departure of all aircraft;
c) aerodrome control service - the provision of control service to aerodrome traffic, except that indicated in item b).
