Forget about the GPL for a moment, and look at copyright. When you fork a project, all code that was present in the original project is copyright of whoever wrote that code in the original project. All code that you write afterwards is your copyright. So unless you re-write all the code from the original project, that code isn't yours and you have no legal rights.
Next you look at the GPL license, and check what rights it gives you beyond the rights of copyright law. It allows you to create derivative works which makes the whole forking business legal in the first place - with plain copyright law, you wouldn't be allowed to create a derivative work. Next, it allows you to use the code as long as you don't distribute it. So as long as nobody else can lay their hands on the forked code, GPL allows you to do what you want with it.
However, if you distribute the forked code, including someone else's copyrighted code, you only have the permission of the copyright holder if you follow their rules. One rule is that you must license the whole code under the GPL (including your own). Another rule is that you must give the source code to others; check the GPL for details.
Changing the license would be difficult, as long as any of the original code is still there. You cannot license your code in a way that prevents the next guy from using the code in the way that GPL allowed, you also can't allow them to do things with the code that GPL doesn't allow.