Fair use is the use of copyrighted material for non-commercial educational or demonstrative purposes. This use also pertains to song parodies so long as the parody is sufficiently different so that it doesn't get mistaken for the original song. If a teacher were giving a lesson about Henry Mancini and wanted to include short excerpts of his music he or she would be allowed to do so under fair use. Another copyright concept is that copyright exists intrinsicly once the work is fixed in a tangible medium. The government does not grant copyrights anymore than it grants basic human rights.
Copyrights exist from the birth of the work forward.
What governments do is register copyrights to prove who owns them and when. The next thing to know about copyrights is that they expire. Works not covered by copyrights are said to be in the public domain. Public domain works can be used by anyone without having to pay royalties as they belong essentially to everyone, i.e. the public. In the United States the current term of copyright is 75 years from the date of copyright.