People can use multiple instances of the same account, that's fine.
The last XMPP instance to connect is the only one that will receive gamelist and rating IQ stanza updates, from what I've seen. Also, the "priority" that each client has, which is often affected by the presence, affects which client receives the gamelist and rating IQ stanzas. When I want to alternate between clients receiving the updates then I find it necessary to reconnect that client to the lobby. And then, yes, there can be a long delay before that client receives updates. That's a known issue, and there's no current solution for it other than to wait for someone (maybe you) to make a change to the game list. That involves changing the visible parameters of a hosted game, changing the users in a hosted game, or creating a new hosted game,
Regarding lack of a rating, it's the same issue as with the game list. Follow the procedure that I described in order to ensure that the client will receive and has received the rating IQ stanza before trying to join or host a game.
There's an improvement in the works, PubSub, that will hopefully resolve this issue so that the above workaround isn't necessary and each instance will receive the gamelist and rating information.