It currently uses Dropbox to share maps and fog information. I do hope to move it to a dedicated server, but I have no experience with servers and those stuff. (assuming you meant this for sharing your screen with other players)
For the player grouping, what you described is how it should work. Selecting a player filter should only show those with the same group value. I’ll look into it.
For the latter, yes I can add that to the special characters list.