Basically, copyright is the legal protection of a item and or property. The most common copyrighted things are software, hardware, tools, books, and clothes. Copyright does not protect things under fair use and or things where the copyright expired and are now under free domain. People buy this licensing from the government and have a seal of approval for whatever they copy-righted.
The public domain is a "center" of people who can make the laws of copy-right. You can find these place near a town hall or somewhere that includes goverment. Work is dedicated to the public domain because everyone revolves around it.
Fair use is when you use something that is already copy-righted and twist it in such a way that makes it significantly different. It fits because it gives opportunity for people to create things with inspiration of other things. Some examples of fair use is royalty free music. Royalty means that musician that made the song gets royalty s/money for every time someone buys that song. A royalty free song means no one gets money and its free to use. This also prevents piracy/stealing from different musicians.
Creativity does builds on the past because we look back on things and we get inspired in and create things. Creative means to create something unique. When creating something, you want to stand out and have something amazing.
Remix changes the meaning of "old" because it changes the product getting remixed. What we mean by that is when creating a "Remixed product" you create another "stem of the tree" from the original product. So usually the new meaning of old means original. We find it to be creative because first it IS different and secondly, it creates opportunity for better things to be created through it.
If your interested on the topic further, this video will give you the basics of the topic!