I would like to know whether any individual belonging to any extinct or extant bird species is conserved in any museum or other place worldwide. Would like to know about genetic studies on this material.
I don't know about birds, but several other types of tetrapods have been studied a lot, including Neanderthal and Denisova hominids, Wooly mammoths and some other mammals. The DNA is often degraded but modern short read deep sequencing techniques have overcome a lot of that problem. With modern human and chimpanzee and gorilla complete genomes plus many Neanderthal and one or a few Denisova genomes plus the extensive human study of hominid fossils and archaeology it is easy to get a picture of some of the genetic issues involved. Point mutation changes in DNA are trivial in comparison to introgression and incomplete lineage sorting, etc.
I propose you to contact museum of frozen animals in Russian Iharka (or Igarka) town. As well I know that with appeard finds from Pleistocene the following labs have to do in Russia:
Laboratory of cryoconserrvation of genetic resource, Institute of cell Biophysics and laboratory of soil Cryology, Institute of physicochemical and biological problems of soil science.
About birds I know exactly about finds of willow grouse only. But direct contact with listed colleagues can help..