Disable Tiger Authentication

File permissions are the big bane of OSX. I only have to authenticate when I am trying to do something in another user account from this one. I suspect your problems originate from how you set up the account and restored files after reverting to Tiger OS. You might be able to get info on a few top level folders that contain your data only and set access permissions on them in Finder Get Info, saying to apply to all enclosed. Be careful in doing this because some items used by applications and the system need special permissions settings.

What are the rights for who on them now?

Have you done the "Repair Permissions" thing in Disk Utility already?

Seeing the authenticate dialog when saving files is not normal.

You may be trying to save into a location that your user does not have permission for. OS X gives you the Home folder for all your personal files. The /Users/Shared folder is designed for files that all users can access. Anywhere outside those locations on the system disk is not intended for your personal files.

The root of the system disk is not intended for your work, if you want to use that location to save you must edit the permissions accordingly, however you want to avoid editing all Apple system folders.

Please report where you are saving files, that will dictate if and how you can repair permissions to fix the issue (there are at least 2 ways to repair permissions in the GUI).

There should be an "Apply to enclosed items..." which I believe should recursively work through enclosed folders. I rarely see this message you are seeing, and as others have observed too, it isn't normal.

Disk Utility's permissions repair only works on standard system and application files and folders, not regular user files.

Related topic with suggestions: Change Permissions Of All Files/Folders At Once?