Your home folder contains literally every file and setting which you, as a standard user, are able to edit, and which your programs (including the Unity desktop environment and/or panels) are able to edit and save their configurations in. It's basically a sealed box, which you and your programs can only get out of if you know your password (which is one of the reasons Ubuntu is so secure - a virus would need it too). This means it contains all settings related to your desktop, and it explains why your panel settings restore to default if you delete it.
In general, don't touch (or delete!) any hidden files in that folder (files starting with a full stop - or period if you're American). Pressing CTRL+h toggles visibility of hidden files.
As for restoring them... if you moved them to the wastebasket, they are easily restored by opening the wastebasket, selecting the files you deleted, and clicking the "Restore Selected Items" button. It will probably ask you if you wish to overwrite the newly created files which replaced them, you do.
If you permanently deleted them, then you permanently deleted them. It would be easier just to change the settings back yourself than to try to recover them.
Also, can you please clarify what you meant by system volume reducing to zero?
Also, the "Restore missing files" option you mentioned only restores from a backup. If you did not make one, you cannot restore it.