You will be asked to provide read permissions to access your public profile information like name and facebook id. Your name is collected only to display it on the welcome message and no other information is collected (your facebook id and some other paublicly accessible data may be fetched by the facebook sdk but they are neither used nor stored) upon login.
You need not give special permissions to share the app page via facebook share button, but sharing your score card on your facebook timeline requires you to grant facebook publishing permission. You can revoke the permissions any time through your facebook app settings. When you share your scorecard, your facebook id and name are sent to the server along with the game details. The server uses your name to print it on your scorecard and the the id to uniquely identify you. The server generates a signed url from your id, name and game details. The unmodified url can be used any time to regenerate the score card. Neither the url nor any information is stored on the server.
Fingerprint: 8F2A 4DCB A280 7A3E EA67 41BC 42FE 98CA FDB2 B7A6