IPhone – How to decline a game invitation from friend

That login banner is a provided aspect of the Game Center API in the iOS SDKs, as far as I'm aware there is no way as a developer to disable it from opening when the Game Center login completes. As a user, there is certainly no way to disable it, because it is part of the application's compiled source code.

However, note that it's not the banner that is causing the delays and skips. It is actually the entire login process to Game Center. My only advice is when you open a game that has Game Center logins, open it up to the first functional screen, and just wait the ~5-10 seconds it takes to reveal the Game Center banner. After the banner has displayed and disappeared, proceed normally and you should not be affected any further.

I guess his device is still logged in with your credentials, and even if you changed the email address or password, his device is still mantaining the session active.

I don't think there's a way to log him off remotely. It seems to me that the only way is a manual log-out on his device.