1. It depends. If you are manually managing your iPhone then all you have to do is hold your finger on any app until they start to shake. Then you click the "x" on the app that you want to delete. If you have it set in iTunes to sync all apps then the next time you sync to iTunes the deleted app will reappear unless you delete it from iTunes or change your settings.
2. You upload a pic to FaceBook within the FB app. If it fails it may be too large or something may be going on with the system (or the app). Try closing the app or perhaps deleting it and then re-installing to see if it helps. I believe with iOS6 you may be able to post pics to FB without entering the app but I may be wrong.