The fans stop because most of the fans sold from RC companies are rated for 5V. Running off of 5 or 6V BEC circuit from ESC or reciever they work fine. These fans typically are brushless DC and the controller burns up. To run direct from battery you need to get a 12V rated DC fan, the only problem with that is it will run slower than rated or won't run at all.
As for the servo, check the manufacturers documents for input support for 7.2V from battery. Some servo's come with extra wire to connect direct from battery. Each manufacturer may have a limit to voltage seen on that connection.
Team Kyosho, Orion, KO Propo America, Avid RC