In Messenger 2011, you can't chat with people while appearing offline [I hate that
], you still are able to do that on Messenger 2009 though.
As for the logging as online, you can cancel the signing in, change your "Log in as" to "Invisible", and then wait for it to complete. You can then sign out [by actually using the "Sign out" link under the menu you can access by clicking your name], it should then set "Invisible" as a new signing in default.
As for the hotmail problem, log in to Hotmail, and click in your name in the upper right corner, choose to Sign out of Messenger, it shouldn't log you in automatically after that.