If you are running v10.6.3 as your profile suggests, update your system soft\ware. Click the Apple menu (top left in your screen) then click: Software Update ...
If you have any Safari third party add ons installed, that could be what's causing the glitch with cookies.
And check Safari / Preferences - Extensions. If you have any installed, turn that off, quit then relaunch Safari.
Try troubleshooting the Safari .plist file.
Quit Safari. Open a Finder window. Select your Home Folder in the Sidebar on the left. It has a small house icon. Then open the Library folder then the Preferences folder. Move the com.apple.Safari.plist file from the Preferences folder to the Desktop. Launch Safari. If that didn't make a difference, move the .plist file back to the Preferences folder.
Try deleting a keychain for one of the sites like Facebook. Quit Safari. Open Keychain Access /Applications/Utilities. Select Passwords on the left. Delete the Facebook keychain. Relaunch Safari. Login to FB. You should be prompted to save your login data to a new keychain, click Yes when prompted. See if you can logout.