What version of FB are you running? You may want to remove from device and reinstall. Have you had this problem before? Was it working before then stopped?
You're doing something wrong. Like I said before, go to the Options icon, click on it. Click on advanced options. Now click on Applications. When the list loads, highlight Facebook and hit the menu key, then click on "Edit Default Permissions" Set at three to allow...
Right, it's pushed to you, but you clicked on it and installed it. Go to Options >Advanced Options >Applicatons. Highlight the Facebook application >Hit Menu >Delete...
1.7 is supposed to be released soon. When you get a FB notification, does it show in the "Messages" icon too? Do you have the email account you use for facebook, on your device?