Regarding the missing(?) backup file I do not understand what you mean. If you are using post-processing, e.g. upload to Dropbox, and you have enabled the delete archive after upload feature (by default it's enabled) then the actual archive is being deleted from your server. Otherwise you're looking at the wrong directory; please look in the output directory you have defined in the profile you are backing up with.
The missing menu item is caused by a known Joomla! bug. Please consult our installation troubleshooting page (it applies to updates, too!) under "Joomla! 1.6/1.7/2.5 installation problems". Please note that on some sites it may be necessary to rename the administrator/components/com_akeeba and/or the components/com_akeeba directories in order for the installation to be completed successfully.
The configuration.php permissions are not touched by Akeeba Backup, therefore I cannot provide any assistance with that. Please consult the Joomla! documentation and its official forum.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!