In Russia a pilot is required to hold a diploma from a state aviation academy in addition to a pilot licence. Exceptions are made only for expat Captains whenever and wherever operationally necessary. I don't think that this is also the case in Ukraine. To the best of my memories, an ICAO licence is considered sufficient qualification for flying commercially in Ukraine.
In terms of visas, Saint Petersburg is an exception from the general legislation, requiring travellers to apply for a visa with the local Russian embassy. There are electronic visas obtained online which only restrict your movement to the city of Saint Petersburg and its administrative unit. However, obtaining a multi-trip business visa for the entire country should not be a problem either.