Question: I press "On Air", select "Stream on Page you manage" but it does not show my pages.
Answer: It very seems you don't accept permissions for JustBroadcaster.
So it's easy steps how to resolve it
Goto Facebook->Settings->Apps or jsut click on this link https://www.facebook.com/settings?tab=applications
Found JustBroadcaster and remove it
Open JustBroadcaster for Facebook and press "On Air". The app will open a browser and it will ask you permissions for JustBroadcaster.
Please press "OK" button for all permissions.
Select your pages or group and press "Start now".
Be aware: you can stream only to you managed pages or group.