Copyright is an exclusive legal right that can be applied to nearly anything that is expressed. It can apply to expressions of facts or ideas (books, movies, products), not the facts or ideas themselves.
Public Domain is something that belongs to the public, therefore it is not under any sort of copyright. For example, the works of Shakespeare and Beethoven are all now part of the public domain, since they were formed before the existence of Copyright.
Fair use is the doctrine in the US copyright law that says brief excerpts of copyrighted material may be used for reasons such as teaching, news reporting, and research without the permission of the creator.
Creativity is built on the past because everything that is created, has been created before. Nothing is truly original because all art (paintings, music, books) are taken from and are extremely influenced by older art. This is clearly understood from the famous quote of William Ralph Inge, "What is originality? Undetected plagiarism."
Due to the fact that everything "new" is some form of a remix, it takes away the uniqueness from the original version. For example the song "Beautiful Girls" by Sean Kingston has the same rhythm as "Stand By Me" by Ben E. King, but for a different purpose. Nowadays people are into more rap and hip-hop type music as opposed to the original song "Stand By Me", so "Beautiful Girls" suits to a more modern audience, while keeping the legend of Ben E. King alive.