* Servers will most likely be the same as the main game, the hosts (GMs) PC is the server. I think that the arena even works this way too, no dedicated servers.
* Characters would be stored on the GMs computer. The current game stores everything in a save file on the host's PC, the GM mode will undoubtedly work the same way.
* GM Mode will most likely handle mods the same way as the main game, but that could get interesting if using mods where the clients need the same mods as the GM.
* Currently depends on the mod, I suspect GM Mode will have a similar limitation.
* Probably not, unless they have plans to use/copy the arena lobby to cater for people looking for other people to play the main campaign or GM mode with.