All of these have been said before really quite a few times. One login server doing the authentication for many game servers is a big advantage, the game server doesnt need to be concerned with authenticating incoming connections to the same degree. Which means that alot less cpu time is spent on it, meaning more can be spent on the actual game packets.
You can host them on separate machines and only expose the game ip address to the client in the packet so if someone decides they are going to attack your server chances are they will attack the auth server and not the game server.