kinda incorrect. while yes the BMW 003 used by the MiG-9 came off the Heinkel 162, and the Junkers Jumo 004 used by the Yak-15 and 17 came from the me-262, they were utilized in the most insane configuration possible by having the engine block underneath the front of the fuselage, and the exhaust about 1/3rd of the way. even when they figured out how to keep the underside of the fuselage from burning they still never really solved the problem of melting runways. hell they should've just copied the me-262 like the japanese did! at least the MiG-9 was a solid fighter though.
MiG 9 and Yak-15 were not "proper" jets, you explained yourself why. They were quickly thrown together prototypes, which both required extensive work to get operational, YAK-15 was an attempt to put jet engines on piston-engined frame.
They did copy ME-262, if flew only half-year later than Yak-15, under the name SU-9. The project, however went nowhere, as MIG-9, with new British engine was deemed better.
MIG-9 wasn`t a decent fighter. It actually lost test fights to pretty much any piston engined fighter, but it was very good versus strategic bombers, presumably the reason SU pushed it into production, as allies had huge fleet.