Hosting is done via TCP/IP, so you should have no trouble doing so locally.

You can hop between hosting your own server, joining others' servers, and playing offline as much as you like, the game is designed to be played that way.

No idea about GOG/Steam interplay, but as long as both platforms are updated to the same version I suspect it will work. Multiplayer backend seems pretty OG, with only minimal Steamworks integration.

Locally hosted servers work and save the same regardless if clients are connecting via WAN or LAN.