Just about any WOW server on private WOW server list is free to join and even free to play. However some private WOW servers offer players to buy upgrades and unlock specific features.
Most of WOW servers have to do that since private servers require powerful hardware and internet connection in order to provide players with enjoyable experience. There are also private WOW servers that are ran purely off donations but most of those don't really invest much in gameplay and new features.
Can I make my own private WOW server?
Sure, just about anyone can, the question is, is it worth it? Running private WOW server is not an easy job and even if you can take care of hardware and software part of it, you still need website for your server and staff team for support.