Yes. Keep your project file on the main system drive, and your media on a separate drive. It is also VERY advisable to back up your project to another drive (such as the media drive) in case your project becomes corrupt or your HD get damaged. This way, if one drive fails, then you have the project backed up on another.
But true. The project file should reside on the main drive. You don’t HAVE to if you don’t want to…there are no issues with keeping it on your external as well. The most important thing is the back up…