The fighter that crashes in Yuri’s village, as far as I can tell from the sources, is likely to have been a Yak 9D, or a close relative.
Russian aircraft tended not to be given romantic names like ‘Spitfire’ or ‘Hurricane’. A ‘Yak’ can be anything from a WW1 biplane to a modern jet, with only the serial number to distinguish them. The name ‘Yak’ is, like most Soviet aircraft names, an abbreviation of the factory’s name, itself usually the name of the founding chief designer, in this case Alexander Sergeyevich Yakovlev.
The 9D is typical of the low-wing, piston-engined fighters of WW2, and looks very similar to its British and American equivalents. It was a fair match in combat for the German’s famous Me109, even though early examples had only basic equipment. The build-quality was also not great. Stalin had relocated the factories to sites further east in the Ural Mountains to protect them from German attacks, and they were working desperately to produce the numbers of aircraft needed.
The Yak that came down in Yuri’s village was making a controlled landing after being damaged in a dog-fight, but one of its undercarriage legs collapsed as a result of getting stuck in the marshy ground. I am guessing this meant it tipped forwards on its nose. Subsequently it was burned to prevent it falling into enemy hands, but the burnt-out wreck was an inspiring object for Yuri’s growing fascination with aircraft.