Will there be support for players to be able to set up their computers as the servers? Possibly for small parties when people have multiple computers but no controllers or when I want to play with a friend who lives near me without having to access a server far away. And also if God forbids, SSF2 servers get shut down.

SSF2's online mode only uses server connectivity for the list of rooms. Once you join the match the connection is direct. We may introduce local lobbyless functionality in an upcoming update but it will not be in Beta.