1) It sounds like you have the Automatically Login Facebook Users feature enabled. If so, when a users visits your site that has already approved your Facebook Application, JFBConnect will act as though they just clicked the "Login With Facebook" button. If you don't want that behavior, you should disable that feature.
There is no Automatically login LinkedIn users feature. There isn't any way that we know that a user should automatically be logged in with their LinkedIn credentials since LinkedIn operates very differently than Facebook.
2) To put those on the same line, try simply adding the following to your template's CSS file:
.logout-button {float:left;}
Hope that helps, but if not, let us know!
Thanks,
Alex