How do I run a server from a .exe file?
Do you mean how to run a unity standalone exe as a headless server?
“my-server.exe -batchmode -nographics”
The default NetworkManagerHUD component lets you click Server only and then you are hosting a server for the game.
How can I have an exe file that hosts the server instead of hosting the server in-game?
Ah, uNet HLAPI - not tried that one. But it would seem that you want to run a dedicated server (one that isn’t also a client). Maybe one of the uNet guys can answer this one?
Hopefully 
TNet also has this feature where you can host a game (server only) from an exe file and then people with the built game can connect to that server.