2. Does Kyrgyz law require the registration of aircrafts?

Yes, however, aircrafts which are registered in another country are not required to be registered in the Kyrgyz Republic.
Meteorological balloons, as well as gliders and aerostats used exclusively for meteorological purposes or to unmanned free balloon or balloons without payload and other similar aircraft are not required to be registered in the Kyrgyz Republic. They are however, still subject to a special accounting procedure by the Civil Aviation Authority. All civil aircrafts which are not registered in a foreign state and which are operated in the Kyrgyz Republic must be registered with the Civil Aviation Authority.