As far as recovering forgotten usernames and passwords, Square Enix do not usually give out this information for security reasons. However, on the login screen in PlayOnline Viewer (if you’re logged in automatically upon starting PlayOnline Viewer, you’ll need to log out to get to this screen), it will probably already have your PlayOnline ID listed on the right hand side under your handle name.
If you log in with this ID, it will ask for your password, which however, is blanked out with asterisks for security reasons. Unfortunately, if you try to change your password in Settings, it will still ask you to enter in your old one before you can change it. Other than maybe trying to get a new one issued by Square Enix, there isn’t really much else that can be done about this, otehr than purchasing a new copy of the game I’m sorry to say.