Editing base C++ classes?

Short answer: You don’t/shouldn’t.

Long answer: You can download the engine source from github and compile the entire engine. Then you can make modifications to the default and have them affect the game. But even then, you really shouldn’t. You should really only modify the engine to address bugs or address some other thing that is lacking that can’t be fixed any other way. You shouldn’t make any gameplay specific changes through engine code.

You could split the difference and copy the default character source code to make MyDefaultCharacter, but then you’ll loose out on any fixes from Epic that are done to the original character class.