Thank you for writing in, we're happy to help clarify this! If you'd like to use Luna Display with a monitor and not have it set up in Headless mode, all you'd need to do is attach the external monitor to your Mac Mini with the proper cable. Your Mac Mini screen will then appear on your external monitor and you can use your iPad as a secondary screen in extended or mirrored mode.
Headless mode will just ensure your iPad is registered as your only display for the Mac Mini; once an external monitor is attached to the Mac Mini, it's no longer registered as the only display. If you'd like to extend or mirror your iPad display, you can adjust this in the Luna Settings under "Luna Display". Under "Set Luna up as:" you can select either "Second display" to extend or "Mirror" to mirror your Mac Mini's screen to the iPad.
If you don't want to use your iPad at all, you would just want to close out of the Luna applications when the external monitor is connected to your Mac Mini. This way, you'll only be using the external monitor as your only display for the Mac Mini.